Boolean-valued Models and Independence Proofs in Set Theory
Author | : John Lane Bell |
Publisher | : Oxford University Press, USA |
Total Pages | : 158 |
Release | : 1977 |
Genre | : Algebra, Boolean |
ISBN | : |
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Author | : John Lane Bell |
Publisher | : Oxford University Press, USA |
Total Pages | : 158 |
Release | : 1977 |
Genre | : Algebra, Boolean |
ISBN | : |
Author | : John L. Bell |
Publisher | : OUP Oxford |
Total Pages | : 216 |
Release | : 2011-05-05 |
Genre | : Mathematics |
ISBN | : 0191620823 |
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.
Author | : John Barkley Rosser |
Publisher | : |
Total Pages | : 248 |
Release | : 1969 |
Genre | : Mathematics |
ISBN | : |
This text shows how to construct models for set theory in which the truth values of statements are elements of a Boolean algebra.
Author | : John L. Bell |
Publisher | : Oxford University Press |
Total Pages | : 214 |
Release | : 2011-05-05 |
Genre | : Computers |
ISBN | : 0199609160 |
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.
Author | : Thomas J. Jech |
Publisher | : Courier Corporation |
Total Pages | : 226 |
Release | : 2008-01-01 |
Genre | : Mathematics |
ISBN | : 0486466248 |
Comprehensive and self-contained text examines the axiom's relative strengths and consequences, including its consistency and independence, relation to permutation models, and examples and counterexamples of its use. 1973 edition.
Author | : Michael Hallett |
Publisher | : Oxford University Press |
Total Pages | : 372 |
Release | : 1986 |
Genre | : Mathematics |
ISBN | : 9780198532835 |
Cantor's ideas formed the basis for set theory and also for the mathematical treatment of the concept of infinity. The philosophical and heuristic framework he developed had a lasting effect on modern mathematics, and is the recurrent theme of this volume. Hallett explores Cantor's ideas and, in particular, their ramifications for Zermelo-Frankel set theory.
Author | : Charles C Pinter |
Publisher | : Courier Corporation |
Total Pages | : 259 |
Release | : 2014-07-23 |
Genre | : Mathematics |
ISBN | : 0486497089 |
"This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--
Author | : Ieke Moerdijk |
Publisher | : Springer |
Total Pages | : 151 |
Release | : 2018-11-23 |
Genre | : Mathematics |
ISBN | : 3319924141 |
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.