Download or read book Notes On Forcing Axioms written by Stevo Todorcevic and published by World Scientific. This book was released on 2013-12-26 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the mathematical practice, the Baire category method is a tool for establishing the existence of a rich array of generic structures. However, in mathematics, the Baire category method is also behind a number of fundamental results such as the Open Mapping Theorem or the Banach-Steinhaus Boundedness Principle. This volume brings the Baire category method to another level of sophistication via the internal version of the set-theoretic forcing technique. It is the first systematic account of applications of the higher forcing axioms with the stress on the technique of building forcing notions rather than on the relationship between different forcing axioms or their consistency strengths.
Download or read book Proceedings of the International Congress of Mathematicians 2010 icm 2010 in 4 Volumes Vol I Plenary Lectures and Ceremonies Vols Ii iv Invited Lectures written by and published by World Scientific. This book was released on 2011 with total page 814 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Topics in Set Theory written by Mohamed Bekkali and published by Springer. This book was released on 1991-07-10 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the Fall Semester of 1987, Stevo Todorcevic gave a series of lectures at the University of Colorado. These notes of the course, taken by the author, give a novel and fast exposition of four chapters of Set Theory. The first two chapters are about the connection between large cardinals and Lebesque measure. The third is on forcing axioms such as Martin's axiom or the Proper Forcing Axiom. The fourth chapter looks at the method of minimal walks and p-functions and their applications. The book is addressed to researchers and graduate students interested in Set Theory, Set-Theoretic Topology and Measure Theory.
Download or read book Combinatorial Set Theory written by Lorenz J. Halbeisen and published by Springer. This book was released on 2017-12-20 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory. Following an overview of basic notions in combinatorics and first-order logic, the author outlines the main topics of classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated technique of forcing in great detail, now including a separate chapter on Suslin’s problem. The technique is used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In the final part, some topics of classical set theory are revisited and further developed in light of forcing, with new chapters on Sacks Forcing and Shelah’s astonishing construction of a model with finitely many Ramsey ultrafilters. Written for graduate students in axiomatic set theory, Combinatorial Set Theory will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists and historical remarks at the end of each chapter, this book is suitable for self-study.
Download or read book Lectures in set theory with particular emphasis on the method of forcing written by Thomas J. Jech and published by . This book was released on 1971 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Foundations of Mathematics written by Kenneth Kunen and published by . This book was released on 2009 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Handbook of Set Theoretic Topology written by K. Kunen and published by Elsevier. This book was released on 2014-06-28 with total page 1282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Juhász on cardinal functions; Roitman and Abraham-Todorčević on S- and L-spaces; Weiss and Baumgartner on versions of Martin's axiom; and Vaughan and Stephenson on compactness properties.
Download or read book The Axiom of Choice written by Thomas J. Jech and published by Courier Corporation. This book was released on 2008-01-01 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Forcing For Mathematicians written by Nik Weaver and published by World Scientific. This book was released on 2014-01-24 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ever since Paul Cohen's spectacular use of the forcing concept to prove the independence of the continuum hypothesis from the standard axioms of set theory, forcing has been seen by the general mathematical community as a subject of great intrinsic interest but one that is technically so forbidding that it is only accessible to specialists. In the past decade, a series of remarkable solutions to long-standing problems in C*-algebra using set-theoretic methods, many achieved by the author and his collaborators, have generated new interest in this subject. This is the first book aimed at explaining forcing to general mathematicians. It simultaneously makes the subject broadly accessible by explaining it in a clear, simple manner, and surveys advanced applications of set theory to mainstream topics.
Download or read book Proper and Improper Forcing written by Saharon Shelah and published by Cambridge University Press. This book was released on 2017-03-23 with total page 1069 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the theory of proper forcing and its relatives from the beginning. No prior knowledge of forcing is required.
Download or read book The Axiom of Determinacy Forcing Axioms and the Nonstationary Ideal written by W. Hugh Woodin and published by Walter de Gruyter. This book was released on 2013-02-01 with total page 944 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of high-level monographs on all areas of mathematical logic and its applications. It is addressed to advanced students and research mathematicians, and may also serve as a guide for lectures and for seminars at the graduate level.
Download or read book The Higher Infinite written by Akihiro Kanamori and published by Springer Science & Business Media. This book was released on 2008-11-23 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the years, this book has become a standard reference and guide in the set theory community. It provides a comprehensive account of the theory of large cardinals from its beginnings and some of the direct outgrowths leading to the frontiers of contemporary research, with open questions and speculations throughout.
Download or read book Introduction to Axiomatic Set Theory written by G. Takeuti and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1963, the first author introduced a course in set theory at the University of Illinois whose main objectives were to cover Godel's work on the con sistency of the Axiom of Choice (AC) and the Generalized Continuum Hypothesis (GCH), and Cohen's work on the independence of the AC and the GCH. Notes taken in 1963 by the second author were taught by him in 1966, revised extensively, and are presented here as an introduction to axiomatic set theory. Texts in set theory frequently develop the subject rapidly moving from key result to key result and suppressing many details. Advocates of the fast development claim at least two advantages. First, key results are high lighted, and second, the student who wishes to master the subject is com pelled to develop the detail on his own. However, an instructor using a "fast development" text must devote much class time to assisting his students in their efforts to bridge gaps in the text.
Download or read book Set Theory and the Continuum Hypothesis written by Paul J. Cohen and published by Courier Corporation. This book was released on 2008-12-09 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This exploration of a notorious mathematical problem is the work of the man who discovered the solution. Written by an award-winning professor at Stanford University, it employs intuitive explanations as well as detailed mathematical proofs in a self-contained treatment. This unique text and reference is suitable for students and professionals. 1966 edition. Copyright renewed 1994.
Download or read book Naive Set Theory written by Paul Halmos and published by . This book was released on 2019-06 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a prominent analyst Paul. R. Halmos, this book is the most famous, popular, and widely used textbook in the subject. The book is readable for its conciseness and clear explanation. This emended edition is with completely new typesetting and corrections. Asymmetry of the book cover is due to a formal display problem. Actual books are printed symmetrically. Please look at the paperback edition for the correct image. The free PDF file available on the publisher's website www.bowwowpress.org
Download or read book The Axiom of Constructibility written by K. J. Devlin and published by Springer. This book was released on 2006-11-15 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Set Theory and the Continuum Problem written by Raymond M. Smullyan and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
