Surveys In Set Theory

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Surveys in Set Theory

Adrian Richard David Mathias,Savilian Professor of Geometry N J Hitchin
Surveys in Set Theory Book PDF

Author : Adrian Richard David Mathias,Savilian Professor of Geometry N J Hitchin
Publisher : Unknown
Page : 257 pages
File Size : 43,5 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1107361036

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Surveys in Set Theory by Adrian Richard David Mathias,Savilian Professor of Geometry N J Hitchin Pdf

This book comprises five expository articles and two research papers on topics of current interest in set theory and the foundations of mathematics. Articles by Baumgartner and Devlin introduce the reader to proper forcing. This is a development by Saharon Shelah of Cohen's method which has led to solutions of problems that resisted attack by forcing methods as originally developed in the 1960s. The article by Guaspari is an introduction to descriptive set theory, a subject that has developed dramatically in the last few years. Articles by Kanamori and Stanley discuss one of the most difficult concepts in contemporary set theory, that of the morass, first created by Ronald Jensen in 1971 to solve the gap-two conjecture in model theory, assuming Godel's axiom of constructibility. The papers by Prikry and Shelah complete the volume by giving the reader the flavour of contemporary research in set theory. This book will be of interest to graduate students and research workers in set theory and mathematical logic.

Surveys in Set Theory

A. R. D. Mathias
Surveys in Set Theory Book PDF

Author : A. R. D. Mathias
Publisher : Cambridge University Press
Page : 257 pages
File Size : 40,7 Mb
Release : 1983-10-13
Category : Mathematics
ISBN : 9780521277334

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Surveys in Set Theory by A. R. D. Mathias Pdf

This book comprises five expository articles and two research papers on topics of current interest in set theory and the foundations of mathematics. Articles by Baumgartner and Devlin introduce the reader to proper forcing. This is a development by Saharon Shelah of Cohen's method which has led to solutions of problems that resisted attack by forcing methods as originally developed in the 1960s. The article by Guaspari is an introduction to descriptive set theory, a subject that has developed dramatically in the last few years. Articles by Kanamori and Stanley discuss one of the most difficult concepts in contemporary set theory, that of the morass, first created by Ronald Jensen in 1971 to solve the gap-two conjecture in model theory, assuming Gödel's axiom of constructibility. The papers by Prikry and Shelah complete the volume by giving the reader the flavour of contemporary research in set theory. This book will be of interest to graduate students and research workers in set theory and mathematical logic.

Surveys in Set Theory

A. R. D. Mathias
Surveys in Set Theory Book PDF

Author : A. R. D. Mathias
Publisher : Unknown
Page : 256 pages
File Size : 44,7 Mb
Release : 1983
Category : Electronic books
ISBN : 1107365945

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Surveys in Set Theory by A. R. D. Mathias Pdf

This book comprises five expository articles and two research papers on topics of current interest in set theory and the foundations of mathematics.

Descriptive Set Theory

Yiannis N. Moschovakis
Descriptive Set Theory Book PDF

Author : Yiannis N. Moschovakis
Publisher : American Mathematical Soc.
Page : 521 pages
File Size : 41,6 Mb
Release : 2009-06-30
Category : Mathematics
ISBN : 9780821848135

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Descriptive Set Theory by Yiannis N. Moschovakis Pdf

Descriptive Set Theory is the study of sets in separable, complete metric spaces that can be defined (or constructed), and so can be expected to have special properties not enjoyed by arbitrary pointsets. This subject was started by the French analysts at the turn of the 20th century, most prominently Lebesgue, and, initially, was concerned primarily with establishing regularity properties of Borel and Lebesgue measurable functions, and analytic, coanalytic, and projective sets. Its rapid development came to a halt in the late 1930s, primarily because it bumped against problems which were independent of classical axiomatic set theory. The field became very active again in the 1960s, with the introduction of strong set-theoretic hypotheses and methods from logic (especially recursion theory), which revolutionized it. This monograph develops Descriptive Set Theory systematically, from its classical roots to the modern ``effective'' theory and the consequences of strong (especially determinacy) hypotheses. The book emphasizes the foundations of the subject, and it sets the stage for the dramatic results (established since the 1980s) relating large cardinals and determinacy or allowing applications of Descriptive Set Theory to classical mathematics. The book includes all the necessary background from (advanced) set theory, logic and recursion theory.

Descriptive Set Theory and the Structure of Sets of Uniqueness

A. S. Kechris,Alain Louveau
Descriptive Set Theory and the Structure of Sets of Uniqueness Book PDF

Author : A. S. Kechris,Alain Louveau
Publisher : Cambridge University Press
Page : 384 pages
File Size : 53,5 Mb
Release : 1987-11-27
Category : Mathematics
ISBN : 0521358116

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Descriptive Set Theory and the Structure of Sets of Uniqueness by A. S. Kechris,Alain Louveau Pdf

To make this work accessible to logicians as well as set theorists and analysts, classical and modern theory of sets of uniqueness are covered as well as the relevant parts of descriptive set theory.

Geometric Set Theory

Paul B. Larson,Jindrich Zapletal
Geometric Set Theory Book PDF

Author : Paul B. Larson,Jindrich Zapletal
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 52,7 Mb
Release : 2020-07-16
Category : Education
ISBN : 9781470454623

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Geometric Set Theory by Paul B. Larson,Jindrich Zapletal Pdf

This book introduces a new research direction in set theory: the study of models of set theory with respect to their extensional overlap or disagreement. In Part I, the method is applied to isolate new distinctions between Borel equivalence relations. Part II contains applications to independence results in Zermelo–Fraenkel set theory without Axiom of Choice. The method makes it possible to classify in great detail various paradoxical objects obtained using the Axiom of Choice; the classifying criterion is a ZF-provable implication between the existence of such objects. The book considers a broad spectrum of objects from analysis, algebra, and combinatorics: ultrafilters, Hamel bases, transcendence bases, colorings of Borel graphs, discontinuous homomorphisms between Polish groups, and many more. The topic is nearly inexhaustible in its variety, and many directions invite further investigation.

Labyrinth of Thought

Jose Ferreiros
Labyrinth of Thought Book PDF

Author : Jose Ferreiros
Publisher : Springer Science & Business Media
Page : 472 pages
File Size : 42,5 Mb
Release : 2001-11-01
Category : Mathematics
ISBN : 3764357495

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Labyrinth of Thought by Jose Ferreiros Pdf

"José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic)

A Survey on Single-Valued Neutrosophic K-Algebras

Muhammad Akram,Kar-Ping Shum
A Survey on Single Valued Neutrosophic K Algebras Book PDF

Author : Muhammad Akram,Kar-Ping Shum
Publisher : Infinite Study
Page : 25 pages
File Size : 44,8 Mb
Release : 2024-06-30
Category : Juvenile Nonfiction
ISBN : 8210379456XXX

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A Survey on Single-Valued Neutrosophic K-Algebras by Muhammad Akram,Kar-Ping Shum Pdf

In this survey, we first present a brief overview of logical algebras. We then discuss concepts of single-valued neutrosophic K-subalgebras, single-valued neutrosophic soft K-algebras and single-valued neutrosophic topological K-algebras. Moreover, we discuss various fundamental concepts which includes interior, closure, C5-connectivity, super connectivity, compactness and Hausdorffness of single-valued neutrosophic topological K-algebras.

Sets and Proofs

S. Barry Cooper,John K. Truss
Sets and Proofs Book PDF

Author : S. Barry Cooper,John K. Truss
Publisher : Cambridge University Press
Page : 450 pages
File Size : 40,6 Mb
Release : 1999-06-17
Category : Mathematics
ISBN : 0521635497

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Sets and Proofs by S. Barry Cooper,John K. Truss Pdf

First of two volumes providing a comprehensive guide to mathematical logic.

The Sage Handbook of Survey Development and Application

Lucy R. Ford,Terri A. Scandura
The Sage Handbook of Survey Development and Application Book PDF

Author : Lucy R. Ford,Terri A. Scandura
Publisher : SAGE Publications Limited
Page : 512 pages
File Size : 47,8 Mb
Release : 2023-06-29
Category : Social Science
ISBN : 9781529618624

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The Sage Handbook of Survey Development and Application by Lucy R. Ford,Terri A. Scandura Pdf

The SAGE Handbook of Survey Development and Application provides a practical resource that researchers can go to for cutting-edge tools to ensure they are employing the best survey research techniques. This handbook not only covers the classic and innovational skills and approaches involved at every step of the survey research process, but also centres itself around applied, how-to guidance to aid readers in best practice. Chapters engage with a broad range of topics including sampling issues, approaches to establishment of measurement equivalence, and the use of online labour pools in survey development. With contributions from a global community of leading and emerging scholars across a wide variety of disciplines, this Handbook is focused on being applicable and accessible across the social sciences. Containing over 120 tables and figures, checklists and tutorial guides, The SAGE Handbook of Survey Development and Application will serve as a one stop resource for survey research. This handbook serves as a touchstone for a variety of fields such as Organizational Behavior, Industrial & Organizational Psychology, Management, Psychology, Educational Research, Marketing, Public Policy, and others. PART 1: Conceptual Issues and Operational Definition PART 2: Research Design Considerations PART 3: Item Development PART 4: Scale Improvement Methods PART 5: Data Collection PART 6: Data Management and Analysis PART 7: Research Production and Dissemination PART 8: Applications

Analytic Number Theory

Yoichi Motohashi
Analytic Number Theory Book PDF

Author : Yoichi Motohashi
Publisher : Cambridge University Press
Page : 396 pages
File Size : 42,5 Mb
Release : 1997-10-16
Category : Mathematics
ISBN : 9780521625128

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Analytic Number Theory by Yoichi Motohashi Pdf

Authoritative, up-to-date review of analytic number theory containing outstanding contributions from leading international figures.

Set Theory

Abhijit Dasgupta
Set Theory Book PDF

Author : Abhijit Dasgupta
Publisher : Springer Science & Business Media
Page : 434 pages
File Size : 50,9 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9781461488545

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Set Theory by Abhijit Dasgupta Pdf

What is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenth-century mathematicians such as Dedekind and Cantor gave birth to set theory. This textbook presents classical set theory in an intuitive but concrete manner. To allow flexibility of topic selection in courses, the book is organized into four relatively independent parts with distinct mathematical flavors. Part I begins with the Dedekind–Peano axioms and ends with the construction of the real numbers. The core Cantor–Dedekind theory of cardinals, orders, and ordinals appears in Part II. Part III focuses on the real continuum. Finally, foundational issues and formal axioms are introduced in Part IV. Each part ends with a postscript chapter discussing topics beyond the scope of the main text, ranging from philosophical remarks to glimpses into landmark results of modern set theory such as the resolution of Lusin's problems on projective sets using determinacy of infinite games and large cardinals. Separating the metamathematical issues into an optional fourth part at the end makes this textbook suitable for students interested in any field of mathematics, not just for those planning to specialize in logic or foundations. There is enough material in the text for a year-long course at the upper-undergraduate level. For shorter one-semester or one-quarter courses, a variety of arrangements of topics are possible. The book will be a useful resource for both experts working in a relevant or adjacent area and beginners wanting to learn set theory via self-study.

Handbook of Set Theory

Matthew Foreman,Akihiro Kanamori
Handbook of Set Theory Book PDF

Author : Matthew Foreman,Akihiro Kanamori
Publisher : Springer Science & Business Media
Page : 2200 pages
File Size : 50,7 Mb
Release : 2009-12-10
Category : Mathematics
ISBN : 9781402057649

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Handbook of Set Theory by Matthew Foreman,Akihiro Kanamori Pdf

Numbers imitate space, which is of such a di?erent nature —Blaise Pascal It is fair to date the study of the foundation of mathematics back to the ancient Greeks. The urge to understand and systematize the mathematics of the time led Euclid to postulate axioms in an early attempt to put geometry on a ?rm footing. With roots in the Elements, the distinctive methodology of mathematics has become proof. Inevitably two questions arise: What are proofs? and What assumptions are proofs based on? The ?rst question, traditionally an internal question of the ?eld of logic, was also wrestled with in antiquity. Aristotle gave his famous syllogistic s- tems, and the Stoics had a nascent propositional logic. This study continued with ?ts and starts, through Boethius, the Arabs and the medieval logicians in Paris and London. The early germs of logic emerged in the context of philosophy and theology. The development of analytic geometry, as exempli?ed by Descartes, ill- tratedoneofthedi?cultiesinherentinfoundingmathematics. Itisclassically phrased as the question ofhow one reconciles the arithmetic with the geom- ric. Arenumbers onetypeofthingand geometricobjectsanother? Whatare the relationships between these two types of objects? How can they interact? Discovery of new types of mathematical objects, such as imaginary numbers and, much later, formal objects such as free groups and formal power series make the problem of ?nding a common playing ?eld for all of mathematics importunate. Several pressures made foundational issues urgent in the 19th century.

Set Theory and the Continuum Problem

Raymond M. Smullyan,Melvin Fitting
Set Theory and the Continuum Problem Book PDF

Author : Raymond M. Smullyan,Melvin Fitting
Publisher : Unknown
Page : 0 pages
File Size : 42,5 Mb
Release : 2010
Category : Continuum hypothesis
ISBN : 0486474844

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Set Theory and the Continuum Problem by Raymond M. Smullyan,Melvin Fitting Pdf

A lucid, elegant, and complete survey of set theory, this three-part treatment explores axiomatic set theory, the consistency of the continuum hypothesis, and forcing and independence results. 1996 edition.

Singularity Theory

Bill Bruce,D. Mond
Singularity Theory Book PDF

Author : Bill Bruce,D. Mond
Publisher : Cambridge University Press
Page : 468 pages
File Size : 44,5 Mb
Release : 1999-06-03
Category : Computers
ISBN : 0521658888

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Singularity Theory by Bill Bruce,D. Mond Pdf

An up-to-date survey of research in singularity theory.