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Books on the topic 'Equivalence classes (Set theory)'

Author: Grafiati

Published: 4 June 2021

Last updated: 16 February 2022

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1

Borel equivalence relations: Structure and classification. Providence, R.I: American Mathematical Society, 2008.

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2

Hjorth, Greg. Classification and orbit equivalence relations. Providence, RI: American Mathematical Society, 2000.

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3

G, Sushkov B., ed. Preobrazovanie logicheskikh funkt͡siĭ na klasse ėkvivalentnykh dvoichnykh derevʹev. Moskva: Vychislitelʹnyĭ t͡sentr AN SSSR, 1986.

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4

Kechris, A. S. Topics in orbit equivalence. Berlin: Springer, 2004.

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5

Castrén, Marcus. Recrel: A similarity measure for set-classes. Helsinki: Sibelius Academy, 1994.

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6

Hjorth, Greg. Rigidity theorems for actions of product groups and countable Borel equivalence relations. Providence, RI: American Mathematical Society, 2005.

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7

K, Lewis David. Parts of classes. Oxford, UK: B. Blackwell, 1991.

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8

Parts of classes. Oxford: Basil Blackwell, 1990.

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9

Fulman, Igor. Crossed products of von Neumann algebras by equivalence relations and their subalgebras. Providence, R.I: American Mathematical Society, 1997.

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10

Weekly Reader Early Learning Library (Firm), ed. I know same and different. Milwaukee: Weekly Reader Early Learning Library, 2006.

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11

I Know Same And Different (I'm Ready for Math). Gareth Stevens Publishing, 2005.

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12

Weekly Reader Early Learning Library (Firm), ed. I know same and different =: Igual y diferente. Milwaukee, WI: Weekly Reader Early Learning Library, 2006.

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13

Kiang, Tsai-Han. The Theory of Fixed Point Classes. Springer, 2014.

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14

Koff, Caroline Nan. A specialized ATMS for equivalence relations. 1988.

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15

Keating, Jon, and Nina Snaith. Random permutations and related topics. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.25.

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This article considers some topics in random permutations and random partitions highlighting analogies with random matrix theory (RMT). An ensemble of random permutations is determined by a probability distribution on Sn, the set of permutations of [n] := {1, 2, . . . , n}. In many ways, the symmetric group Sn is linked to classical matrix groups. Ensembles of random permutations should be given the same treatment as random matrix ensembles, such as the ensembles of classical compact groups and symmetric spaces of compact type with normalized invariant measure. The article first describes the Ewens measures, virtual permutations, and the Poisson-Dirichlet distributions before discussing results related to the Plancherel measure on the set of equivalence classes of irreducible representations of Sn and its consecutive generalizations: the z-measures and the Schur measures.

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16

Castren, Marcus. Recrel: A similarity measure for set-classes (Studia musica). Sibelius Academy, 1994.

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17

Castren, Marcus. Recrel: A similarity measure for set-classes (Studia musica). Sibelius Academy, 1994.

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18

Eileen, Denza. Classes of Heads of Mission. Oxford University Press, 2016. http://dx.doi.org/10.1093/law/9780198703969.003.0015.

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This chapter analyses Articles 14 and 15 of the Vienna Convention on Diplomatic Relations. Article 14 organizes the heads of the diplomatic of each respective State into three classes, namely: (a) that of ambassadors or nuncios (in the case of the Holy See) accredited to Heads of State and other heads of mission of equivalent rank; (b) that of envoys, ministers and internuncios accredited to Heads of State; and (c) that of chargés d’affaires accredited to Ministers for Foreign Affairs. The Article also makes it clear that there shall be no differentiation between heads of mission by reason of their class. Article 15 further concerns the classes of the heads of mission as it states that the classes to be assigned shall be agreed between the States. The chapter also looks into how the International Law Commission faced the concerns surrounding the classes leading up to the formation of both Articles.

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19

Zhou, Yiqiang, and John Dauns. Classes of Modules. Taylor & Francis Group, 2006.

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20

Crupi, Vincenzo, and Katya Tentori. Confirmation Theory. Edited by Alan Hájek and Christopher Hitchcock. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199607617.013.33.

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We first discuss several qualitative properties of confirmation as analyzed in a probabilistic framework. Some of these properties are classical, while others are relatively novel; some are shared by absolute and incremental confirmation, others are distinctive for each kind. We then proceed to address axiomatic characterizations of major classes of probabilistic measures of incremental confirmation. This treatment includes an original result displaying how conditions which single out the traditional probability difference measure up to ordinal equivalence. Finally, we argue that the longstanding project of a compelling confirmation-theoretic generalization of logical entailment (and refutation) can be achieved, provided that the right explicatum is adopted (to wit, a relative distance measure). This conclusion, we submit, dispels concerns that have been aired in the literature up to recent times.

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21

Classes of Modules (Pure and Applied Mathematics). Chapman & Hall/CRC, 2006.

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22

Alqassas, Ahmad. A Unified Theory of Polarity Sensitivity. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780197554883.001.0001.

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This book examines polarity sensitivity—a ubiquitous phenomenon involving expressions such as anybody, nobody, ever, never, and somebody and their counterparts in other languages, with particular focus on Arabic. These expressions belong to different classes such as negative and positive polarity, negative concord, and negative indefinites, which led to examining their syntax and semantics separately. In this book, Ahmad Alqassas pursues a unified approach that relies on examining the interaction between the various types of polarity sensitivity. Treating this interaction is fundamental for scrutinizing their licensing conditions. Alqassas draws on data from Standard Arabic and the major regional dialects represented by Jordanian, Egyptian, Moroccan, and Qatari. The book provides a new perspective on the syntax–semantic interface and develops a unified syntactic analysis for polarity sensitivity. Through the (micro)comparative approach, Alqassas explains the distributional contrasts with a minimal set of universal syntactic operations such as Merge, Move, and Agree, and a fine-grained inventory of negative formal features for polarity items and their licensors. The features are simple invisibles that paint a complex landscape of polarity. The results suggest that syntactic computation of Arabic polarity (externally merged in the left periphery) is subservient to the conceptual–intentional interface. Alqassas argues for last resort insertion of covert negation operators in the CP layer to interpret non-strict NCIs, which is an extra mechanism that serves the semantic interface but adds to the complexity of syntactic computation. Likewise, head NPIs in the left periphery require licensing by operators higher than the tense phrase, adding more constraints on the syntactic licensing.

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23

Caramello, Olivia. Introduction. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198758914.003.0002.

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This book is devoted to a general study of geometric theories through the associated classifying toposes.A central theme of the book is a duality, established in Chapter 3, between the subtoposes of the classifying topos of a geometric theory T over a signature ∑ and the (syntactic-equivalence classes of) ‘quotients’ of the theory ...

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24

Gilbert, Margaret. Contemporary Rights Theories. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198813767.003.0006.

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The most influential theories of claims within contemporary rights theory are considered in relation to the demand-right problem. Starting with Hohfeld’s equivalence, contemporary theorists generally aim for an account of claims such that the members of a certain canonical set of claim-ascriptions are true. In pursuit of this aim they tend to focus on directed duties and to assume that these are in part constituted by plain duties. Reviewing the results obtained by adopting this aim and method, this chapter argues that in order to solve the demand-right problem we need to go beyond the resources of Thomson’s constraint theory, Joseph Raz’s “interest” theory, and similar views. The same goes for Hart’s “choice” theory and related positions, and several other approaches more briefly considered.

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25

Ward, Colleen, Taciano L. Milfont, and Ype H. Poortinga. Methodological Considerations for Comparative Research on Acculturation and Health. Edited by Seth J. Schwartz and Jennifer Unger. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780190215217.013.13.

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This chapter outlines standards and best practices for designing cross-cultural and cross-ethnic comparative investigations of acculturation and health. It distinguishes two streams of research—public health (epidemiological studies) and those that focus on theory-testing (socio-behavioral studies); provides an overview of acculturation measures, including an analysis of the strengths and weaknesses of various assessment techniques; and briefly describes common approaches to the assessment of health and health-related behaviors. It describes how to set up studies that meet high standards, addressing key issues in defining populations in comparative studies, sampling, and the need for careful data collection procedures; describes various research designs, emphasizing the need for control of extraneous variables; and specifically highlights issues of equivalence and how bias can be identified and avoided. Finally, it summarizes challenges faced by researchers and describes new initiatives that might address some of the common shortcomings of comparative studies of acculturation and health.

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26

Boudreau, Joseph F., and Eric S. Swanson. Templates, the standard C++ library, and modern C++. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198708636.003.0017.

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This chapter is devoted to programming techniques which rely on the C++ template mechanism. This mechanism, which is the basis of a computing style known as generic programming, allows whole families of functions and classes to be easily written. It is described early in the chapter. A host of extremely useful template functions and classes is universally available in the C++ standard library, including container classes (vector, list, set, and map) and algorithms used to sort, shuffle, and otherwise manipulate or query their contents. The chapter closes with an introduction to the newer constructs of modern C++: smart pointers, lambda functions, the auto keyword, range-based for loops, and more. An application to group theory is explored in the exercises.

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27

Martín-Vide, Carlos. Formal Grammars and Languages. Edited by Ruslan Mitkov. Oxford University Press, 2012. http://dx.doi.org/10.1093/oxfordhb/9780199276349.013.0008.

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This article introduces the preliminaries of classical formal language theory. It outlines the main classes of grammars as language-generating devices and automata as language-recognizing devices. It offers a number of definitions and examples and presents the basic results. It classifies grammar according to several criteria. The most widespread one is the form of their productions. This article presents a systematic study of the common properties of language families has led to the theory of abstract families of languages. It shows that a context-free grammar generates not only a set of strings, but a set of trees too: each one of the trees is associated with a string and illustrates the way this string is derived in the grammar.

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28

Asudeh, Ash, and Gianluca Giorgolo. Enriched Meanings. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198847854.001.0001.

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This book presents a theory of enriched meanings for natural language interpretation. Certain expressions that exhibit complex effects at the semantics/pragmatics boundary live in an enriched meaning space while others live in a more basic meaning space. These basic meanings are mapped to enriched meanings just when required compositionally, which avoids generalizing meanings to the worst case. The theory is captured formally using monads, a concept from category theory. Monads are also prominent in functional programming and have been successfully used in the semantics of programming languages to characterize certain classes of computation. They are used here to model certain challenging linguistic computations at the semantics/pragmatics boundary. Part I presents some background on the semantics/pragmatics boundary, informally presents the theory of enriched meanings, reviews the linguistic phenomena of interest, and provides the necessary background on category theory and monads. Part II provides novel compositional analyses of the following phenomena: conventional implicature, substitution puzzles, and conjunction fallacies. Part III explores the prospects of combining monads, with particular reference to these three cases. The authors show that the compositional properties of monads model linguistic intuitions about these cases particularly well. The book is an interdisciplinary contribution to Cognitive Science: These phenomena cross not just the boundary between semantics and pragmatics, but also disciplinary boundaries between Linguistics, Philosophy and Psychology, three of the major branches of Cognitive Science, and are here analyzed with techniques that are prominent in Computer Science, a fourth major branch. A number of exercises are provided to aid understanding, as well as a set of computational tools (available at the book's website), which also allow readers to develop their own analyses of enriched meanings.

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29

Grace, Nancy M., ed. The Beats. Liverpool University Press, 2021. http://dx.doi.org/10.3828/liverpool/9781949979954.001.0001.

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This volume is the first-ever collection devoted to teaching Beat literature in high school to graduate-level classes. Essays address teaching topics such as the history of the censorship of Beat writing, Beat spirituality, the small press revolution, Beat composition techniques and ELL, Beat multiculturalism/globalism and its legacies, techno-poetics, the road tale, Beat drug use, the Italian-American Beat heritage, Beats and the visual arts of the 1960s, the Beat and Black Mountain confluence, Beat comedy, Beat performance poetry, Beat creative non-fiction, West coast-East/coast Beat communities, and Beat representations of race, gender, class, and ethnicity. Individual essays focus on Gary Snyder’s ecopoetics, William S. Burroughs’s post- and transhumanism, Jack Kerouac’s On the Road (teaching it in the U.S. and abroad) and his Quebecois novels, Allen Ginsberg, Diane di Prima, ruth weiss, Joyce Johnson, Joanne Kyger, Bob Kaufman, and Anne Waldman. Many additional Beat-associated writers, such as Amiri Baraka Gregory Corso, are featured in the other essays. The collection opens with a comprehensive essay by Nancy M. Grace on a history of Beat literature, its reception in and out of academia, and contemporary approaches to teaching Beat literature in multidisciplinary contexts. Many of the essays highlight online resources and other materials proven useful in the classroom. Critical methods range from feminism/gender theory, to critical race theory, formalism, historiography, religious studies, and transnational theory to reception theory. The volume concludes with selected scholarly resources, both primary and secondary, including films, music, and other art forms; and a set of Beat-related classroom assignments recommended by active Beat scholars and teachers.

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30

Brown, Deborah J., and Calvin G. Normore. Descartes and the Ontology of Everyday Life. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198836810.001.0001.

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Far from being the founder of an austere reductionism, Descartes is committed to a rich, multilayered, and complex metaphysics. This book begins by locating Descartes’s work against the ancient and medieval background to which he is reacting. It proceeds to argue that his theory of distinctions requires what he explicitly endorses―that in addition to minds and modes, there are material substances of every size. These substances when appropriately configured form automata, self-sustaining, functionally integrated systems of which animals and human bodies are important sub-classes. Descartes’ conception of function, which is crucial to his characterization of these uniquely organized collections of matter, is shown to be compatible with his rejection of final causes in natural science, and gives him resources to account for composite beings which are not themselves substances. It is argued that besides automata, these composites include individual human beings, which are unions of minds and bodies individuated by minds. The unique modes which characterize the union, in particular, its passions, set the foundation for a social ontology that includes genuine social entities such as families and nation states. Societies are forged by individuals in acts of willing to join in union with others that Descartes takes to be of the essence of love. The result is a picture of Descartes very different from the myths that have come to surround him.

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