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Set Theory An Introduction To Independence Proofs

Set Theory An Introduction To Independence Proofs Author K. Kunen
ISBN-10 9780080570587
Release 2014-06-28
Pages 330
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Studies in Logic and the Foundations of Mathematics, Volume 102: Set Theory: An Introduction to Independence Proofs offers an introduction to relative consistency proofs in axiomatic set theory, including combinatorics, sets, trees, and forcing. The book first tackles the foundations of set theory and infinitary combinatorics. Discussions focus on the Suslin problem, Martin's axiom, almost disjoint and quasi-disjoint sets, trees, extensionality and comprehension, relations, functions, and well-ordering, ordinals, cardinals, and real numbers. The manuscript then ponders on well-founded sets and easy consistency proofs, including relativization, absoluteness, reflection theorems, properties of well-founded sets, and induction and recursion on well-founded relations. The publication examines constructible sets, forcing, and iterated forcing. Topics include Easton forcing, general iterated forcing, Cohen model, forcing with partial functions of larger cardinality, forcing with finite partial functions, and general extensions. The manuscript is a dependable source of information for mathematicians and researchers interested in set theory.

Set Theory

Set Theory Author Kenneth Kunen
ISBN-10 0444854010
Release 1980-01-01
Pages 313
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Set Theory has been writing in one form or another for most of life. You can find so many inspiration from Set Theory also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Set Theory book for free.

Provability Computability and Reflection

Provability  Computability and Reflection Author Lev D. Beklemishev
ISBN-10 0080955037
Release 2000-04-01
Pages 577
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Provability, Computability and Reflection

Recursion Theory

Recursion Theory Author Chi Tat Chong
ISBN-10 9783110275643
Release 2015-08-17
Pages 320
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This monograph presents recursion theory from a generalized and largely global point of view. A major theme is the study of the structures of degrees arising from two key notions of reducibility, the Turing degrees and the hyperdegrees, using ideas and techniques beyond those of classical recursion theory. These include structure theory, hyperarithmetic determinacy and rigidity, basis theorems, independence results on Turing degrees, as well as applications to higher randomness.

Descriptive Topology in Selected Topics of Functional Analysis

Descriptive Topology in Selected Topics of Functional Analysis Author Jerzy Kąkol
ISBN-10 9781461405290
Release 2011-08-30
Pages 496
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"Descriptive Topology in Selected Topics of Functional Analysis" is a collection of recent developments in the field of descriptive topology, specifically focused on the classes of infinite-dimensional topological vector spaces that appear in functional analysis. Such spaces include Fréchet spaces, (LF)-spaces and their duals, and the space of continuous real-valued functions C(X) on a completely regular Hausdorff space X, to name a few. These vector spaces appear in functional analysis in distribution theory, differential equations, complex analysis, and various other analytical settings. This monograph provides new insights into the connections between the topological properties of linear function spaces and their applications in functional analysis.

Introduction to Cardinal Arithmetic

Introduction to Cardinal Arithmetic Author Michael Holz
ISBN-10 9783034603300
Release 2010-04-06
Pages 304
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This book is an introduction to modern cardinal arithmetic, developed in the frame of the axioms of Zermelo-Fraenkel set theory together with the axiom of choice. It splits into three parts. Part one, which is contained in Chapter 1, describes the classical cardinal arithmetic due to Bernstein, Cantor, Hausdorff, Konig, and Tarski. The results were found in the years between 1870 and 1930. Part two, which is Chapter 2, characterizes the development of cardinal arith metic in the seventies, which was led by Galvin, Hajnal, and Silver. The third part, contained in Chapters 3 to 9, presents the fundamental investigations in pcf-theory which has been developed by S. Shelah to answer the questions left open in the seventies. All theorems presented in Chapter 3 and Chapters 5 to 9 are due to Shelah, unless otherwise stated. We are greatly indebted to all those set theorists whose work we have tried to expound. Concerning the literature we owe very much to S. Shelah's book [Sh5] and to the article by M. R. Burke and M. Magidor [BM] which also initiated our students' interest for Shelah's pcf-theory.

Classical Descriptive Set Theory

Classical Descriptive Set Theory Author Alexander Kechris
ISBN-10 9781461241904
Release 2012-12-06
Pages 404
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Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text presents a largely balanced approach to the subject, which combines many elements of the different traditions. It includes a wide variety of examples, more than 400 exercises, and applications, in order to illustrate the general concepts and results of the theory.

Set Theory for the Working Mathematician

Set Theory for the Working Mathematician Author Krzysztof Ciesielski
ISBN-10 0521594650
Release 1997-08-28
Pages 236
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Presents those methods of modern set theory most applicable to other areas of pure mathematics.

The Foundations of Mathematics

The Foundations of Mathematics Author Kenneth Kunen
ISBN-10 1904987141
Release 2009
Pages 251
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Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Lowenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continues the foundational issues begun in the set theory chapter. Mathematics can now be viewed as formal proofs from ZFC. Also, model theory leads to models of set theory. This includes a discussion of absoluteness, and an analysis of models such as H( ) and R( ). The Recursion Theory chapter develops some basic facts about computable functions, and uses them to prove a number of results of foundational importance; in particular, Church's theorem on the undecidability of logical consequence, the incompleteness theorems of Godel, and Tarski's theorem on the non-definability of truth.

Notes on Set Theory

Notes on Set Theory Author Yiannis N. Moschovakis
ISBN-10 3540941800
Release 1994-01-01
Pages 272
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The axiomatic theory of sets is a vibrant part of pure mathematics, with its own basic notions, fundamental results, and deep open problems. It is also viewed as a foundation of mathematics so that "to make a notion precise" simply means "to define it in set theory." This book gives a solid introduction to "pure set theory" through transfinite recursion and the construction of the cumulative hierarchy of sets, and also attempts to explain how mathematical objects can be faithfully modeled within the universe of sets. In this new edition the author has added solutions to the exercises, and rearranged and reworked the text to improve the presentation.

Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century Author Paolo Mancosu
ISBN-10 9780195132441
Release 1999
Pages 275
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The seventeenth century saw dramatic advances in mathematical theory and practice than any era before or since. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, analytic geometry, the geometry of indivisibles, the arithmetic of infinites, and the calculus had been developed. Although many technical studies have been devoted to these innovations, Paolo Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Beginning with the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes' Geometrie, the relationship between empiricist epistemology and infinitistic theorems in geometry, and the debates concerning the foundations of the Leibnizian calculus In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics.

Fundamentals of Mathematical Logic

Fundamentals of Mathematical Logic Author Peter G. Hinman
ISBN-10 1568812620
Release 2005-09-09
Pages 896
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This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Gödel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory. Based on the author's more than 35 years of teaching experience, the book develops students' intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic.

The Bulletin of Symbolic Logic

The Bulletin of Symbolic Logic Author
ISBN-10 UOM:39015072636981
Release 2008
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The Bulletin of Symbolic Logic has been writing in one form or another for most of life. You can find so many inspiration from The Bulletin of Symbolic Logic also informative, and entertaining. Click DOWNLOAD or Read Online button to get full The Bulletin of Symbolic Logic book for free.

Principles of Mathematics

Principles of Mathematics Author Vladimir Lepetic
ISBN-10 9781119131656
Release 2015-11-30
Pages 672
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Presents a uniquely balanced approach that bridges introductory and advanced topics in modern mathematics An accessible treatment of the fundamentals of modern mathematics, Principles of Mathematics: A Primer provides a unique approach to introductory andadvanced mathematical topics. The book features six main subjects, whichcan be studied independently or in conjunction with each other including: settheory; mathematical logic; proof theory; group theory; theory of functions; andlinear algebra. The author begins with comprehensive coverage of the necessary building blocks in mathematics and emphasizes the need to think abstractly and develop an appreciation for mathematical thinking. Maintaining a useful balance of introductory coverage and mathematical rigor, Principles of Mathematics: A Primer features: Detailed explanations of important theorems and their applications Hundreds of completely solved problems throughout each chapter Numerous exercises at the end of each chapter to encourage further exploration Discussions of interesting and provocative issues that spark readers’ curiosity and facilitate a better understanding and appreciation of the field of mathematics Principles of Mathematics: A Primer is an ideal textbook for upper-undergraduate courses in the foundations of mathematics and mathematical logic as well as for graduate-level courses related to physics, engineering, and computer science. The book is also a useful reference for readers interested in pursuing careers in mathematics and the sciences. Vladimir Lepetic, PhD, is Professor in the Department of Mathematical Sciences at DePaul University. His research interests include mathematical physics, set theory, foundations of mathematics, and the philosophy of mathematics.

Handbook of Set theoretic Topology

Handbook of Set theoretic Topology Author Kenneth Kunen
ISBN-10 UOM:39076000658778
Release 1984
Pages 1273
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This Handbook is an introduction to set-theoretic topology for students in the field and for researchers in other areas for whom results in set-theoretic topology may be relevant. The aim of the editors has been to make it as self-contained as possible without repeating material which can easily be found in standard texts. The Handbook contains detailed proofs of core results, and references to the literature for peripheral results where space was insufficient. Included are many open problems of current interest.In general, the articles may be read in any order. In a few cases they occur in pairs, with the first one giving an elementary treatment of a subject and the second one more advanced results. These pairs are: Hodel and Juhaacute;sz on cardinal functions; Roitman and Abraham-Todorccaron;evicacute; on S- and L-spaces; Weiss and Baumgartner on versions of Martin's axiom; and Vaughan and Stephenson on compactness properties.

Notices of the American Mathematical Society

Notices of the American Mathematical Society Author
ISBN-10 UCAL:B3647861
Release 1984
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Notices of the American Mathematical Society has been writing in one form or another for most of life. You can find so many inspiration from Notices of the American Mathematical Society also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Notices of the American Mathematical Society book for free.

Pacific Journal of Mathematics

Pacific Journal of Mathematics Author
ISBN-10 UCAL:B4474055
Release 2001-10
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Pacific Journal of Mathematics has been writing in one form or another for most of life. You can find so many inspiration from Pacific Journal of Mathematics also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Pacific Journal of Mathematics book for free.