Log in

Relevant bibliographies by topics / Axiom of choice / Journal articles

To see the other types of publications on this topic, follow the link: Axiom of choice.

Journal articles on the topic 'Axiom of choice'

Author: Grafiati

Published: 4 June 2021

Last updated: 4 March 2023

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Axiom of choice.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

MORILLON, MARIANNE. "MULTIPLE CHOICES IMPLY THE INGLETON AND KREIN–MILMAN AXIOMS." Journal of Symbolic Logic 85, no. 1 (July 12, 2019): 439–55. http://dx.doi.org/10.1017/jsl.2019.48.

Full text

Abstract:

AbstractIn set theory without the Axiom of Choice, we consider Ingleton’s axiom which is the ultrametric counterpart of the Hahn–Banach axiom. We show that in ZFA, i.e., in the set theory without the Axiom of Choice weakened to allow “atoms,” Ingleton’s axiom does not imply the Axiom of Choice (this solves in ZFA a question raised by van Rooij, [27]). We also prove that in ZFA, the “multiple choice” axiom implies the Krein–Milman axiom. We deduce that, in ZFA, the conjunction of the Hahn–Banach, Ingleton and Krein–Milman axioms does not imply the Axiom of Choice.

APA, Harvard, Vancouver, ISO, and other styles

2

van Lambalgen, Michiel. "Independence, randomness and the axiom of choice." Journal of Symbolic Logic 57, no. 4 (December 1992): 1274–304. http://dx.doi.org/10.2307/2275368.

Full text

Abstract:

AbstractWe investigate various ways of introducing axioms for randomness in set theory. The results show that these axioms, when added to ZF, imply the failure of AC. But the axiom of extensionality plays an essential role in the derivation, and a deeper analysis may ultimately show that randomness is incompatible with extensionality.

APA, Harvard, Vancouver, ISO, and other styles

3

Halbeisen, Lorenz, and Saharon Shelah. "Relations Between Some Cardinals in the Absence of the Axiom of Choice." Bulletin of Symbolic Logic 7, no. 2 (June 2001): 237–61. http://dx.doi.org/10.2307/2687776.

Full text

Abstract:

AbstractIf we assume the axiom of choice, then every two cardinal numbers are comparable. In the absence of the axiom of choice, this is no longer so. For a few cardinalities related to an arbitrary infinite set, we will give all the possible relationships between them, where possible means that the relationship is consistent with the axioms of set theory. Further we investigate the relationships between some other cardinal numbers in specific permutation models and give some results provable without using the axiom of choice.

APA, Harvard, Vancouver, ISO, and other styles

4

Campbell, Donald E. "Arrow's choice axiom." Economics Letters 44, no. 4 (April 1994): 381–84. http://dx.doi.org/10.1016/0165-1765(94)90107-4.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Luce, R. "Luce's choice axiom." Scholarpedia 3, no. 12 (2008): 8077. http://dx.doi.org/10.4249/scholarpedia.8077.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

Liao, Yu-Hsien. "Relative Symmetric Reductions under Multi-Choice Non-Transferable-Utility Situations." Mathematics 10, no. 5 (February 22, 2022): 682. http://dx.doi.org/10.3390/math10050682.

Full text

Abstract:

In many game-theoretical results, the reduction axiom and its converse have been regarded as important requirements under axiomatic processes for solutions. However, it is shown that the replicated core counters a specific (inferior) converse reduction axiom under multi-choice non-transferable-utility situations. Thus, two modified reductions and relative properties of the reduction axiom and its converse are proposed to characterize the replicated core in this article.The main methods and relative results are as follows. First, two different types of reductions are proposed by focusing on both participants and participation levels under relative symmetric reducing behavior. Further, relative reduction axioms and their converse are adopted to characterize the replicated core.

APA, Harvard, Vancouver, ISO, and other styles

7

Pallares Vega, Ivonne. "Sets, Properties and Truth Values: A Category-Theoretic Approach to Zermelo’s Axiom of Separation." Athens Journal of Philosophy 1, no. 3 (September 2, 2022): 135–62. http://dx.doi.org/10.30958/ajphil.1-3-2.

Full text

Abstract:

In 1908 the German mathematician Ernst Zermelo gave an axiomatization of the concept of set. His axioms remain at the core of what became to be known as Zermelo-Fraenkel set theory. There were two axioms that received diverse criticisms at the time: the axiom of choice and the axiom of separation. This paper centers around one question this latter axiom raised. The main purpose is to show how this question might be solved with the aid of another, more recent mathematical theory of sets which, like Zermelo’s, has numerous philosophical underpinnings. Keywords: properties of sets, foundations of mathematics, axiom of separation, subobject classifier, truth values

APA, Harvard, Vancouver, ISO, and other styles

8

Dihoum, Eman, and Michael Rathjen. "Preservation of choice principles under realizability." Logic Journal of the IGPL 27, no. 5 (February 8, 2019): 746–65. http://dx.doi.org/10.1093/jigpal/jzz002.

Full text

Abstract:

AbstractEspecially nice models of intuitionistic set theories are realizability models $V({\mathcal A})$, where $\mathcal A$ is an applicative structure or partial combinatory algebra. This paper is concerned with the preservation of various choice principles in $V({\mathcal A})$ if assumed in the underlying universe $V$, adopting Constructive Zermelo–Fraenkel as background theory for all of these investigations. Examples of choice principles are the axiom schemes of countable choice, dependent choice, relativized dependent choice and the presentation axiom. It is shown that any of these axioms holds in $V(\mathcal{A})$ for every applicative structure $\mathcal A$ if it holds in the background universe.1 It is also shown that a weak form of the countable axiom of choice, $\textbf{AC}^{\boldsymbol{\omega , \omega }}$, is rendered true in any $V(\mathcal{A})$ regardless of whether it holds in the background universe. The paper extends work by McCarty (1984, Realizability and Recursive Mathematics, PhD Thesis) and Rathjen (2006, Realizability for constructive Zermelo–Fraenkel set theory. In Logic Colloquium 03, pp. 282–314).

APA, Harvard, Vancouver, ISO, and other styles

9

Blavatskyy, Pavlo R. "Dual choice axiom and probabilistic choice." Journal of Risk and Uncertainty 61, no. 1 (August 2020): 25–41. http://dx.doi.org/10.1007/s11166-020-09332-7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

Doğan, Battal. "How to Control Controlled School Choice: Comment." American Economic Review 107, no. 4 (April 1, 2017): 1362–64. http://dx.doi.org/10.1257/aer.20160913.

Full text

Abstract:

Echenique and Yenmez (2015), in Theorem 2, characterize choice rules that are “generated by reserves for the priority.” We show that the “only if” part is not correct. We exhibit a choice rule that is generated by reserves for the priority but violates one of their axioms. We reformulate the axiom and repair the result. (JEL D47, H75, I21, I28)

APA, Harvard, Vancouver, ISO, and other styles

11

Rich, Patricia. "Hybrid Vigor." Erasmus Journal for Philosophy and Economics 11, no. 1 (July 19, 2018): 1–30. http://dx.doi.org/10.23941/ejpe.v11i1.284.

Full text

Abstract:

The ecological approach to rationality involves evaluating choice processes instead of choices themselves, and there are good reasons for doing this. Proponents of the ecological approach insist that objective performance criteria (such as monetary gains) replace axiomatic criteria, but this claim is highly contentious. This paper investigates these issues through a case study: 12 risky choice processes are simulated, and their performance records are compared. The first criterion is conformity to the Expected Utility axioms; the Priority Heuristic stands out for frequently violating Transitivity. Next, the Expected Value criterion is applied. Minimax performs especially poorly—despite never violating an axiom—highlighting the tension between axiomatic (coherence) and objective (correspondence) criteria. Finally, I show that axiom violations carry high costs in terms of expected value. Accordingly, coherence does not guarantee objectively high performance, but incoherence does guarantee diminished performance.

APA, Harvard, Vancouver, ISO, and other styles

12

Taskovic, Milan. "Axiom of choice: 100th next." Mathematica Moravica, no. 8-1 (2004): 39–62. http://dx.doi.org/10.5937/matmor0401039t.

Full text

APA, Harvard, Vancouver, ISO, and other styles

13

Taskovic, Milan. "The axiom of infinite choice." Mathematica Moravica 16, no. 1 (2012): 1–32. http://dx.doi.org/10.5937/matmor1201001t.

Full text

APA, Harvard, Vancouver, ISO, and other styles

14

Anderson, Simon P., and André de Palma. "Oligopoly and Luce's Choice Axiom." Regional Science and Urban Economics 42, no. 6 (November 2012): 1053–60. http://dx.doi.org/10.1016/j.regsciurbeco.2011.10.002.

Full text

APA, Harvard, Vancouver, ISO, and other styles

15

Desai, Santosh, and Rupali Potdar. "Full Rationality of Fuzzy Choice Functions on Base Domain Through Indicators." New Mathematics and Natural Computation 12, no. 03 (October 5, 2016): 175–89. http://dx.doi.org/10.1142/s1793005716500125.

Full text

Abstract:

This paper introduces indicators of the weak fuzzy T-congruence axiom and the fuzzy Chernoff axiom. These indicators measure the degree to which the fuzzy choice function satisfies the weak fuzzy T-congruence axiom and the fuzzy Chernoff axiom. The indicator of the full rationality is expressed in terms of indicators of weak fuzzy T-congruence axiom and the fuzzy Chernoff axiom.

APA, Harvard, Vancouver, ISO, and other styles

16

DESAI, S. S., and S. R. CHAUDHARI. "ON THE FULL RATIONALITY OF FUZZY CHOICE FUNCTIONS ON BASE DOMAIN." New Mathematics and Natural Computation 08, no. 02 (June 14, 2012): 183–93. http://dx.doi.org/10.1142/s1793005712400108.

Full text

Abstract:

The aim of this paper is to discuss the full rationality of fuzzy choice functions defined on base domain. For this purpose, we introduce weak fuzzy T-congruence axiom. We characterize full rationality of fuzzy choice functions in terms of this axiom and the fuzzy Chernoff axiom. Also, we prove that G-rational fuzzy choice functions with transitive rationalizations satisfying fuzzy Chernoff axiom characterizes their full rationality.

APA, Harvard, Vancouver, ISO, and other styles

17

Howard, Paul, and Jean E. Rubin. "The axiom of choice for well-ordered families and for families of well-orderable sets." Journal of Symbolic Logic 60, no. 4 (December 1995): 1115–17. http://dx.doi.org/10.2307/2275876.

Full text

Abstract:

AbstractWe show that it is not possible to construct a Fraenkel-Mostowski model in which the axiom of choice for well-ordered families of sets and the axiom of choice for sets of well-orderable sets are both true, but the axiom of choice is false.

APA, Harvard, Vancouver, ISO, and other styles

18

CUTOLO, RAFFAELLA. "BERKELEY CARDINALS AND THE STRUCTURE OF L(Vδ+1)." Journal of Symbolic Logic 83, no. 04 (December 2018): 1457–76. http://dx.doi.org/10.1017/jsl.2018.35.

Full text

Abstract:

AbstractWe explore the structural properties of the inner model L(Vδ+1) under the assumption that δ is a singular limit of Berkeley cardinals each of which is itself limit of extendible cardinals, lifting some of the main results of the theory of the axiom I0 to the level of Berkeley cardinals, the strongest known large cardinal axioms. Berkeley cardinals have been recently introduced in [1] and contradict the Axiom of Choice.1 In fact, our background theory will be ZF.

APA, Harvard, Vancouver, ISO, and other styles

19

Morillon, Marianne. "Notions of compactness for special subsets of ℝI and some weak forms of the axiom of choice." Journal of Symbolic Logic 75, no. 1 (March 2010): 255–68. http://dx.doi.org/10.2178/jsl/1264433919.

Full text

Abstract:

AbstractWe work in set-theory without choice ZF. A set is countable if it is finite or equipotent with ℕ. Given a closed subset F of [0, 1]I which is a bounded subset of ℓ1(I) (resp. such that F ⊆ c0(I)), we show that the countable axiom of choice for finite sets, (resp. the countable axiom of choice ACℕ) implies that F is compact. This enhances previous results where ACℕ (resp. the axiom of Dependent Choices) was required. If I is linearly orderable (for example I = ℝ), then, in ZF, the closed unit ball of the Hilbert space ℓ2 (I) is (Loeb-)compact in the weak topology. However, the weak compactness of the closed unit ball of is not provable in ZF.

APA, Harvard, Vancouver, ISO, and other styles

20

Spector, Mitchell. "Ultrapowers Without the Axiom of Choice." Journal of Symbolic Logic 53, no. 4 (December 1988): 1208. http://dx.doi.org/10.2307/2274614.

Full text

APA, Harvard, Vancouver, ISO, and other styles

21

Spector, Mitchell. "Ultrapowers without the axiom of choice." Journal of Symbolic Logic 53, no. 4 (December 1988): 1208–19. http://dx.doi.org/10.1017/s0022481200028024.

Full text

Abstract:

AbstractA new method is presented for constructing models of set theory, using a technique of forming pseudo-ultrapowers. In the presence of the axiom of choice, the traditional ultrapower construction has proven to be extremely powerful in set theory and model theory; if the axiom of choice is not assumed, the fundamental theorem of ultrapowers may fail, causing the ultrapower to lose almost all of its utility. The pseudo-ultrapower is designed so that the fundamental theorem holds even if choice fails; this is arranged by means of an application of the omitting types theorem. The general theory of pseudo-ultrapowers is developed. Following that, we study supercompactness in the absence of choice, and we analyze pseudo-ultrapowers of models of the axiom of determinateness and various infinite exponent partition relations. Relationships between pseudo-ultrapowers and forcing are also discussed.

APA, Harvard, Vancouver, ISO, and other styles

22

Judah, Haim, and Saharon Shelah. "Baire property and axiom of choice." Israel Journal of Mathematics 84, no. 3 (October 1993): 435–50. http://dx.doi.org/10.1007/bf02760952.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

Martensen, Erich. "Riesz theory without axiom of choice." Proceedings of the American Mathematical Society 99, no. 3 (March 1, 1987): 496. http://dx.doi.org/10.1090/s0002-9939-1987-0875387-x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

24

Cruz, Omar De la, Eric J. Hall, Paul Howard, Kyriakos Keremedis, and Jean E. Rubin. "Unions and the axiom of choice." Mathematical Logic Quarterly 54, no. 6 (November 4, 2008): 652–65. http://dx.doi.org/10.1002/malq.200710073.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Esser, Olivier. "Inconsistency of the Axiom of Choice with the positive theory." Journal of Symbolic Logic 65, no. 4 (December 2000): 1911–16. http://dx.doi.org/10.2307/2695086.

Full text

Abstract:

AbstractThe idea of the positive theory is to avoid the Russell's paradox by postulating an axiom scheme of comprehension for formulas without “too much” negations. In this paper, we show that the axiom of choice is inconsistent with the positive theory .

APA, Harvard, Vancouver, ISO, and other styles

26

Cerreia-Vioglio, S., F. Maccheroni, M. Marinacci, and A. Rustichini. "Law of demand and stochastic choice." Theory and Decision 92, no. 3-4 (November 8, 2021): 513–29. http://dx.doi.org/10.1007/s11238-021-09844-x.

Full text

Abstract:

AbstractWe consider random choice rules that, by satisfying a weak form of Luce’s choice axiom, embody a form probabilistic rationality. We show that for this important class of stochastic choices, the law of demand for normal goods—arguably the main result of traditional consumer theory—continues to hold on average when strictly dominated alternatives are dismissed.

APA, Harvard, Vancouver, ISO, and other styles

27

Freiling, Chris. "Axioms of symmetry: Throwing darts at the real number line." Journal of Symbolic Logic 51, no. 1 (March 1986): 190–200. http://dx.doi.org/10.2307/2273955.

Full text

Abstract:

AbstractWe will give a simple philosophical “proof” of the negation of Cantor's continuum hypothesis (CH). (A formal proof for or against CH from the axioms of ZFC is impossible; see Cohen [1].) We will assume the axioms of ZFC together with intuitively clear axioms which are based on some intuition of Stuart Davidson and an old theorem of Sierpiński and are justified by the symmetry in a thought experiment throwing darts at the real number line. We will in fact show why there must be an infinity of cardinalities between the integers and the reals. We will also show why Martin's Axiom must be false, and we will prove the extension of Fubini's Theorem for Lebesgue measure where joint measurability is not assumed. Following the philosophy—if you reject CH you are only two steps away from rejecting the axiom of choice (AC)—we will point out along the way some extensions of our intuition which contradict AC.

APA, Harvard, Vancouver, ISO, and other styles

28

Hrbacek, Karel, and Mikhail G. Katz. "Infinitesimal analysis without the Axiom of Choice." Annals of Pure and Applied Logic 172, no. 6 (June 2021): 102959. http://dx.doi.org/10.1016/j.apal.2021.102959.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Cantini, Andrea. "The axiom of choice and combinatory logic." Journal of Symbolic Logic 68, no. 4 (December 2003): 1091–108. http://dx.doi.org/10.2178/jsl/1067620175.

Full text

Abstract:

AbstractWe combine a variety of constructive methods (including forcing, realizability, asymmetric interpretation), to obtain consistency results concerning combinatory logic with extensionality and (forms of) the axiom of choice.

APA, Harvard, Vancouver, ISO, and other styles

30

McCartan, S. D. "Topological Equivalents of the Axiom of Choice." Irish Mathematical Society Bulletin 0021 (1988): 45–48. http://dx.doi.org/10.33232/bims.0021.45.48.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Pincus, David, Herman Rubin, and Jean E. Rubin. "Equivalents of the Axiom of Choice, II." Journal of Symbolic Logic 52, no. 3 (September 1987): 867. http://dx.doi.org/10.2307/2274372.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Blass, Andreas, Ioanna M. Dimitriou, and Benedikt Löwe. "Inaccessible cardinals without the axiom of choice." Fundamenta Mathematicae 194, no. 2 (2007): 179–89. http://dx.doi.org/10.4064/fm194-2-3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

33

Marianne, Morillon. "Linear extenders and the Axiom of Choice." Commentationes Mathematicae Universitatis Carolinae 58, no. 4 (January 5, 2018): 419–34. http://dx.doi.org/10.14712/1213-7243.2015.223.

Full text

APA, Harvard, Vancouver, ISO, and other styles

34

Saari, Donald G. "The profile structure for Luce's choice axiom." Journal of Mathematical Psychology 49, no. 3 (June 2005): 226–53. http://dx.doi.org/10.1016/j.jmp.2005.03.004.

Full text

APA, Harvard, Vancouver, ISO, and other styles

35

Akis, Vladimir N. "The axiom of choice and almost continuity." Topology and its Applications 29, no. 2 (July 1988): 141–50. http://dx.doi.org/10.1016/0166-8641(88)90071-5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

36

Pollard, Stephen. "Plural quantification and the axiom of choice." Philosophical Studies 54, no. 3 (November 1988): 393–97. http://dx.doi.org/10.1007/bf00646278.

Full text

APA, Harvard, Vancouver, ISO, and other styles

37

Gutierres, Gonçalo. "Total Boundedness and the Axiom of Choice." Applied Categorical Structures 24, no. 5 (August 15, 2016): 457–69. http://dx.doi.org/10.1007/s10485-016-9443-1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

38

Galvin, F., and P. Komjáth. "Graph colorings and the axiom of choice." Periodica Mathematica Hungarica 22, no. 1 (February 1991): 71–75. http://dx.doi.org/10.1007/bf02309111.

Full text

APA, Harvard, Vancouver, ISO, and other styles

39

Kleppmann, Philipp. "Nielsen-Schreier and the Axiom of Choice." Mathematical Logic Quarterly 61, no. 6 (October 7, 2015): 458–65. http://dx.doi.org/10.1002/malq.201400046.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Tachtsis, Eleftherios. "On Martin's Axiom and Forms of Choice." Mathematical Logic Quarterly 62, no. 3 (April 13, 2016): 190–203. http://dx.doi.org/10.1002/malq.201400115.

Full text

APA, Harvard, Vancouver, ISO, and other styles

41

Tachtsis, Eleftherios. "Łoś's theorem and the axiom of choice." Mathematical Logic Quarterly 65, no. 3 (September 30, 2019): 280–92. http://dx.doi.org/10.1002/malq.201700074.

Full text

APA, Harvard, Vancouver, ISO, and other styles

42

Aguilera, J. P. "Determinate logic and the Axiom of Choice." Annals of Pure and Applied Logic 171, no. 2 (February 2020): 102745. http://dx.doi.org/10.1016/j.apal.2019.102745.

Full text

APA, Harvard, Vancouver, ISO, and other styles

43

Brunner, Norbert, and Paul Howard. "RUSSELL'S ALTERNATIVE TO THE AXIOM OF CHOICE." Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 38, no. 1 (1992): 529–34. http://dx.doi.org/10.1002/malq.19920380149.

Full text

APA, Harvard, Vancouver, ISO, and other styles

44

Brunner, Norbert, Karl Svozil, and Matthias Baaz. "The Axiom of Choice in Quantum Theory." Mathematical Logic Quarterly 42, no. 1 (1996): 319–40. http://dx.doi.org/10.1002/malq.19960420128.

Full text

APA, Harvard, Vancouver, ISO, and other styles

45

De la Cruz, Omar, Eric Hall, Paul Howard, Kyriakos Keremedis, and Jean E. Rubin. "Metric spaces and the axiom of choice." MLQ 49, no. 5 (September 2003): 455–66. http://dx.doi.org/10.1002/malq.200310049.

Full text

APA, Harvard, Vancouver, ISO, and other styles

46

Tselishchev, Vitaliy V., and Alexander V. Khlebalin. "The Gap between the Intensional and Extensional in Mathematics." Siberian Journal of Philosophy 18, no. 2 (2020): 48–58. http://dx.doi.org/10.25205/2541-7517-2020-18-2-48-58.

Full text

Abstract:

The paper is devoted to the study of the divergence of the intensionalist and extensionalist traditions in the foundations of mathematics. One of the important manifestations of this discrepancy was the debate on the status of the Axiom of Choice. In particular, we argue that Russell's challenging Axioms of the Choice is connected with his intensionalist philosophy of mathematics and the extensionalist approach of Zermelo. It is shown that the opposition of the intensionalist and extensionalist approaches includes such key problems of the philosophy of mathematics as the epistemological features of theorems and axioms, the nature of logical-philosophical analysis, and the role of logic in mathematics.

APA, Harvard, Vancouver, ISO, and other styles

47

Forster, Thomas. "Erdős-Rado without choice." Journal of Symbolic Logic 72, no. 3 (September 2007): 897–900. http://dx.doi.org/10.2178/jsl/1191333846.

Full text

Abstract:

AbstractA version of the Erdős-Rado theorem on partitions of the unordered n-tuples from uncountable sets is proved, without using the axiom of choice. The case with exponent 1 is just the Sierpinski-Hartogs' result that .

APA, Harvard, Vancouver, ISO, and other styles

48

Kanovei, Vladimir, and Vassily Lyubetsky. "On the Significance of Parameters in the Choice and Collection Schemata in the 2nd Order Peano Arithmetic." Mathematics 11, no. 3 (February 1, 2023): 726. http://dx.doi.org/10.3390/math11030726.

Full text

Abstract:

We make use of generalized iterations of the Sacks forcing to define cardinal-preserving generic extensions of the constructible universe L in which the axioms of ZF hold and in addition either (1) the parameter-free countable axiom of choice ACω* fails, or (2) ACω* holds but the full countable axiom of choice ACω fails in the domain of reals. In another generic extension of L, we define a set X⊆P(ω), which is a model of the parameter-free part PA2* of the 2nd order Peano arithmetic PA2, in which CA(Σ21) (Comprehension for Σ21 formulas with parameters) holds, yet an instance of Comprehension CA for a more complex formula fails. Treating the iterated Sacks forcing as a class forcing over Lω1, we infer the following consistency results as corollaries. If the 2nd order Peano arithmetic PA2 is formally consistent then so are the theories: (1) PA2+¬ACω*, (2) PA2+ACω*+¬ACω, (3) PA2*+CA(Σ21)+¬CA.

APA, Harvard, Vancouver, ISO, and other styles

49

Freeman, David J. "Expectations-Based Reference-Dependence and Choice Under Risk." Economic Journal 129, no. 622 (January 8, 2019): 2424–58. http://dx.doi.org/10.1111/ecoj.12639.

Full text

Abstract:

Abstract This article characterises the behavioural content of a model of choice under risk with reference-dependent preferences and endogenous expectations-based reference points based on the preferred personal equilibrium model of Kőszegi and Rabin (2006). The combination of reference-dependent preferences and endogenous reference points leads to violations of the Independence Axiom and can also lead to violations of the Weak Axiom of Revealed Preference. An axiomatic characterisation shows that the model places testable restrictions on choice under risk.

APA, Harvard, Vancouver, ISO, and other styles

50

Howard, Paul. "Unions of well-ordered sets." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 56, no. 1 (February 1994): 117–24. http://dx.doi.org/10.1017/s1446788700034753.

Full text

Abstract:

AbstractIn Zermelo-Fraenkel set theory weakened to permit the existence of atoms and without the axiom of choice we investigate the deductive strength of five statements which make assertions about the cardinality of the union of a well-ordered collection of sets. All five of the statements considered are consequences of the axiom of choice.

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!