set theory an introduction to independence proofs 102 studies in logic and the foundations of mathematics

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Set Theory An Introduction To Independence Proofs

Author : K. Kunen
ISBN : 9780080570587
Genre : Mathematics
File Size : 79. 42 MB
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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.

Einf Hrung In Die Kategorientheorie

Author : Martin Brandenburg
ISBN : 9783662535219
Genre : Mathematics
File Size : 87. 10 MB
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Die Kategorientheorie deckt die innere Architektur der Mathematik auf. Dabei werden die strukturellen Gemeinsamkeiten zwischen mathematischen Disziplinen und ihren spezifischen Konstruktionen herausgearbeitet. Dieses Buch gibt eine systematische Einführung in die Grundbegriffe der Kategorientheorie. Zahlreiche ausführliche Erklärungstexte sowie die große Menge an Beispielen helfen beim Einstieg in diese verhältnismäßig abstrakte Theorie. Es werden viele konkrete Anwendungen besprochen, welche die Nützlichkeit der Kategorientheorie im mathematischen Alltag belegen. Jedes Kapitel wird mit einem motivierenden Text eingeleitet und mit einer großen Aufgabensammlung abgeschlossen. An Vorwissen muss der Leser lediglich ein paar Grundbegriffe des Mathematik-Studiums mitbringen. Die vorliegende zweite vollständig durchgesehene Auflage ist um ausführliche Lösungen zu ausgewählten Aufgaben ergänzt.

Set Theory

Author : Kenneth Kunen
ISBN : 0444854010
Genre : Mathematics
File Size : 62. 9 MB
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Recursion Theory

Author : Chi Tat Chong
ISBN : 9783110275643
Genre : Mathematics
File Size : 28. 11 MB
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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.

Introduction To Cardinal Arithmetic

Author : Michael Holz
ISBN : 9783034603300
Genre : Mathematics
File Size : 75. 53 MB
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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.

Fundamentals Of Mathematical Logic

Author : Peter G. Hinman
ISBN : 1568812620
Genre : Mathematics
File Size : 90. 48 MB
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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

Author :
ISBN : UOM:39015079802636
Genre : Logic, Symbolic and mathematical
File Size : 21. 24 MB
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Notices Of The American Mathematical Society

Author :
ISBN : UCAL:B3647861
Genre : Mathematics
File Size : 27. 61 MB
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Handbook Of Set Theoretic Topology

Author : Kenneth Kunen
ISBN : UOM:39076000658778
Genre : Mathematics
File Size : 61. 45 MB
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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.

Pacific Journal Of Mathematics

Author :
ISBN : UCAL:B4474055
Genre : Mathematics
File Size : 27. 41 MB
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