Download or read book Boolean valued Models and Independence Proofs in Set Theory written by John Lane Bell and published by Oxford University Press, USA. This book was released on 1977 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Set Theory written by John L. Bell and published by OUP Oxford. This book was released on 2011-05-05 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third edition, now available in paperback, is a follow up to the author's classic Boolean-Valued Models and Independence Proofs in Set Theory,. It provides an exposition of some of the most important results in set theory obtained in the 20th century: the independence of the continuum hypothesis and the axiom of choice. Aimed at graduate students and researchers in mathematics, mathematical logic, philosophy, and computer science, the third edition has been extensively updated with expanded introductory material, new chapters, and a new appendix on category theory. It covers recent developments in the field and contains numerous exercises, along with updated and increased coverage of the background material. This new paperback edition includes additional corrections and, for the first time, will make this landmark text accessible to students in logic and set theory.
Download or read book Simplified Independence Proofs written by John Barkley Rosser and published by . This book was released on 1969 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text shows how to construct models for set theory in which the truth values of statements are elements of a Boolean algebra.
Download or read book Boolean valued Models and independence proofs in set theory written by John L. Bell and published by . This book was released on 1979 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Set Theory An Introduction To Independence Proofs written by K. Kunen and published by Elsevier. This book was released on 2014-06-28 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Logic Set Theory Boolean valued Models and Several Independence Proofs in ZF and ZFC written by Joshua Phillip Finkler and published by . This book was released on 1991 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Simplified Independence Proofs written by J. Barkley Rosser and published by . This book was released on 1969 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Simplified Independence Proofs written by John Barkley Rosser (Sr., prof. mathematics) and published by . This book was released on 1969 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lectures in Set Theory written by Thomas J. Jech and published by Springer. This book was released on 2006-11-15 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Set Theory written by John L. Bell and published by Oxford University Press. This book was released on 2011-05-05 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third edition, now available in paperback, is a follow up to the author's classic Boolean-Valued Models and Independence Proofs in Set Theory,. It provides an exposition of some of the most important results in set theory obtained in the 20th century: the independence of the continuum hypothesis and the axiom of choice. Aimed at graduate students and researchers in mathematics, mathematical logic, philosophy, and computer science, the third edition has been extensively updated with expanded introductory material, new chapters, and a new appendix on category theory. It covers recent developments in the field and contains numerous exercises, along with updated and increased coverage of the background material. This new paperback edition includes additional corrections and, for the first time, will make this landmark text accessible to students in logic and set theory.
Download or read book Boolean valued Models of Set Theory when the Boolean Algebra is a Proper Class in the Ground Model written by Donald Hector Pelletier and published by . This book was released on 1971 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Axiomatic Set Theory written by G. Takeuti and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text deals with three basic techniques for constructing models of Zermelo-Fraenkel set theory: relative constructibility, Cohen's forcing, and Scott-Solovay's method of Boolean valued models. Our main concern will be the development of a unified theory that encompasses these techniques in one comprehensive framework. Consequently we will focus on certain funda mental and intrinsic relations between these methods of model construction. Extensive applications will not be treated here. This text is a continuation of our book, "I ntroduction to Axiomatic Set Theory," Springer-Verlag, 1971; indeed the two texts were originally planned as a single volume. The content of this volume is essentially that of a course taught by the first author at the University of Illinois in the spring of 1969. From the first author's lectures, a first draft was prepared by Klaus Gloede with the assistance of Donald Pelletier and the second author. This draft was then rcvised by the first author assisted by Hisao Tanaka. The introductory material was prepared by the second author who was also responsible for the general style of exposition throughout the text. We have inc1uded in the introductory material al1 the results from Boolean algebra and topology that we need. When notation from our first volume is introduced, it is accompanied with a deflnition, usually in a footnote. Consequently a reader who is familiar with elementary set theory will find this text quite self-contained.
Download or read book Set Theory written by Kenneth Kunen and published by . This book was released on 2011 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed for readers who know elementary mathematical logic and axiomatic set theory, and who want to learn more about set theory. The primary focus of the book is on the independence proofs. Most famous among these is the independence of the Continuum Hypothesis (CH); that is, there are models of the axioms of set theory (ZFC) in which CH is true, and other models in which CH is false. More generally, cardinal exponentiation on the regular cardinals can consistently be anything not contradicting the classical theorems of Cantor and König. The basic methods for the independence proofs are the notion of constructibility, introduced by Gödel, and the method of forcing, introduced by Cohen. This book describes these methods in detail, verifi es the basic independence results for cardinal exponentiation, and also applies these methods to prove the independence of various mathematical questions in measure theory and general topology. Before the chapters on forcing, there is a fairly long chapter on "infi nitary combinatorics". This consists of just mathematical theorems (not independence results), but it stresses the areas of mathematics where set-theoretic topics (such as cardinal arithmetic) are relevant. There is, in fact, an interplay between infi nitary combinatorics and independence proofs. Infi nitary combinatorics suggests many set-theoretic questions that turn out to be independent of ZFC, but it also provides the basic tools used in forcing arguments. In particular, Martin's Axiom, which is one of the topics under infi nitary combinatorics, introduces many of the basic ingredients of forcing.
Download or read book Handbook of Philosophical Logic written by D.M. Gabbay and published by Springer Science & Business Media. This book was released on 2005-12-15 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of the Handbook of Philosophical Logic (four volumes) was published in the period 1983-1989 and has proven to be an invaluable reference work to both students and researchers in formal philosophy, language and logic. The second edition of the Handbook is intended to comprise some 18 volumes and will provide a very up-to-date authoritative, in-depth coverage of all major topics in philosophical logic and its applications in many cutting-edge fields relating to computer science, language, argumentation, etc. The volumes will no longer be as topic-oriented as with the first edition because of the way the subject has evolved over the last 15 years or so. However the volumes will follow some natural groupings of chapters. Audience: Students and researchers whose work or interests involve philosophical logic and its applications
Download or read book Second Siberian Winter School Algebra and Analysis written by Igorʹ Aleksandrovich Aleksandrov and published by American Mathematical Soc.. This book was released on 1992 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, the second in the series of porceedings of Soviet Regional Conferences, contains papers presented at the Second Siberian Winter School; Algebra and Analysis, held at Tomsk State University in 1989. The papers touch on a variety of topics, including Lie algebras and Lie groups, sheaves, and automorphic forms.
Download or read book From Sets and Types to Topology and Analysis written by Laura Crosilla and published by Clarendon Press. This book was released on 2005-10-06 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited collection bridges the foundations and practice of constructive mathematics and focusses on the contrast between the theoretical developments, which have been most useful for computer science (eg constructive set and type theories), and more specific efforts on constructive analysis, algebra and topology. Aimed at academic logicians, mathematicians, philosophers and computer scientists Including, with contributions from leading researchers, it is up-to-date, highly topical and broad in scope. This is the latest volume in the Oxford Logic Guides, which also includes: 41. J.M. Dunn and G. Hardegree: Algebraic Methods in Philosophical Logic 42. H. Rott: Change, Choice and Inference: A study of belief revision and nonmonotoic reasoning 43. Johnstone: Sketches of an Elephant: A topos theory compendium, volume 1 44. Johnstone: Sketches of an Elephant: A topos theory compendium, volume 2 45. David J. Pym and Eike Ritter: Reductive Logic and Proof Search: Proof theory, semantics and control 46. D.M. Gabbay and L. Maksimova: Interpolation and Definability: Modal and Intuitionistic Logics 47. John L. Bell: Set Theory: Boolean-valued models and independence proofs, third edition
Download or read book Sets Models and Proofs written by Ieke Moerdijk and published by Springer. This book was released on 2018-11-23 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a concise and self-contained introduction to mathematical logic, with a focus on the fundamental topics in first-order logic and model theory. Including examples from several areas of mathematics (algebra, linear algebra and analysis), the book illustrates the relevance and usefulness of logic in the study of these subject areas. The authors start with an exposition of set theory and the axiom of choice as used in everyday mathematics. Proceeding at a gentle pace, they go on to present some of the first important results in model theory, followed by a careful exposition of Gentzen-style natural deduction and a detailed proof of Gödel’s completeness theorem for first-order logic. The book then explores the formal axiom system of Zermelo and Fraenkel before concluding with an extensive list of suggestions for further study. The present volume is primarily aimed at mathematics students who are already familiar with basic analysis, algebra and linear algebra. It contains numerous exercises of varying difficulty and can be used for self-study, though it is ideally suited as a text for a one-semester university course in the second or third year.
