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Journal articles

Academic literature on the topic 'Inductive sets'

Author: Grafiati

Published: 4 June 2021

Last updated: 10 February 2022

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Journal articles on the topic "Inductive sets"

1

Lubarsky, Robert S. "μ-definable sets of integers". Journal of Symbolic Logic 58, № 1 (1993): 291–313. http://dx.doi.org/10.2307/2275338.

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Inductive definability has been studied for some time already. Nonetheless, there are some simple questions that seem to have been overlooked. In particular, there is the problem of the expressibility of the μ-calculus.The μ-calculus originated with Scott and DeBakker [SD] and was developed by Hitchcock and Park [HP], Park [Pa], Kozen [K], and others. It is a language for including inductive definitions with first-order logic. One can think of a formula in first-order logic (with one free variable) as defining a subset of the universe, the set of elements that make it true. Then “and” correspo

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2

Bosch, Carlos, and Jan Kučera. "Closed bounded sets in inductive limits of $\Cal K$-spaces." Czechoslovak Mathematical Journal 43, no. 2 (1993): 221–23. http://dx.doi.org/10.21136/cmj.1993.128401.

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3

Bell, John L. "Finite sets and frege structures." Journal of Symbolic Logic 64, no. 4 (1999): 1552–56. http://dx.doi.org/10.2307/2586795.

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Call a family of subsets of a set E inductive if and is closed under unions with disjoint singletons, that is, ifA Frege structure is a pair (E, ν) with ν a map to E whose domain dom(ν) is an inductive family of subsets of E such thatIn [2] it is shown in a constructive setting that each Frege structure determines a subset which is the domain of a model of Peano's axioms. In this note we establish, within the same constructive setting, three facts. First, we show that the least inductive family of subsets of a set E is precisely the family of decidable Kuratowski finite subsets of E. Secondly,

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4

CURI, GIOVANNI. "ABSTRACT INDUCTIVE AND CO-INDUCTIVE DEFINITIONS." Journal of Symbolic Logic 83, no. 2 (2018): 598–616. http://dx.doi.org/10.1017/jsl.2018.13.

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AbstractIn [G. Curi, On Tarski’s fixed point theorem. Proc. Amer. Math. Soc., 143 (2015), pp. 4439–4455], a notion of abstract inductive definition is formulated to extend Aczel’s theory of inductive definitions to the setting of complete lattices. In this article, after discussing a further extension of the theory to structures of much larger size than complete lattices, as the class of all sets or the class of ordinals, a similar generalization is carried out for the theory of co-inductive definitions on a set. As a corollary, a constructive version of the general form of Tarski’s fixed poin

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5

ARCISZEWSKI, TOMASZ, and WOJCIECH ZIARKO. "Inductive Learning in Civil Engineering: Rough Sets Approach." Computer-Aided Civil and Infrastructure Engineering 5, no. 1 (2008): 19–28. http://dx.doi.org/10.1111/j.1467-8667.1990.tb00038.x.

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6

Dybjer, Peter. "A general formulation of simultaneous inductive-recursive definitions in type theory." Journal of Symbolic Logic 65, no. 2 (2000): 525–49. http://dx.doi.org/10.2307/2586554.

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AbstractThe first example of a simultaneous inductive-recursive definition in intuitionistic type theory is Martin-Löfs universe à la Tarski. A set U0of codes for small sets is generated inductively at the same time as a function T0, which maps a code to the corresponding small set, is defined by recursion on the way the elements of U0are generated.In this paper we argue that there is an underlyinggeneralnotion of simultaneous inductive-recursive definition which is implicit in Martin-Löf's intuitionistic type theory. We extend previously given schematic formulations of inductive definitions i

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7

Zanger, Daniel Z. "Talagrand’s inductive method and isoperimetric inequalities involving random sets." Statistics & Probability Letters 78, no. 7 (2008): 861–68. http://dx.doi.org/10.1016/j.spl.2007.09.012.

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8

Korobeĭnik, Yu F. "INDUCTIVE AND PROJECTIVE TOPOLOGIES. SUFFICIENT SETS AND REPRESENTING SYSTEMS." Mathematics of the USSR-Izvestiya 28, no. 3 (1987): 529–54. http://dx.doi.org/10.1070/im1987v028n03abeh000896.

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9

Alexandru, Andrei, and Gabriel Ciobanu. "Fuzzy Results for Finitely Supported Structures." Mathematics 9, no. 14 (2021): 1651. http://dx.doi.org/10.3390/math9141651.

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We present a survey of some results published recently by the authors regarding the fuzzy aspects of finitely supported structures. Considering the notion of finite support, we introduce a new degree of membership association between a crisp set and a finitely supported function modelling a degree of membership for each element in the crisp set. We define and study the notions of invariant set, invariant complete lattices, invariant monoids and invariant strong inductive sets. The finitely supported (fuzzy) subgroups of an invariant group, as well as the L-fuzzy sets on an invariant set (with

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10

LUMSDAINE, PETER LEFANU, and MICHAEL SHULMAN. "Semantics of higher inductive types." Mathematical Proceedings of the Cambridge Philosophical Society 169, no. 1 (2019): 159–208. http://dx.doi.org/10.1017/s030500411900015x.

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AbstractHigher inductive typesare a class of type-forming rules, introduced to provide basic (and not-so-basic) homotopy-theoretic constructions in a type-theoretic style. They have proven very fruitful for the “synthetic” development of homotopy theory within type theory, as well as in formalising ordinary set-level mathematics in type theory. In this paper, we construct models of a wide range of higher inductive types in a fairly wide range of settings.We introduce the notion ofcell monad with parameters: a semantically-defined scheme for specifying homotopically well-behaved notions of stru

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