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 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 1070 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the fifth publication in the Perspectives in Logic series, studies set-theoretic independence results (independence from the usual set-theoretic ZFC axioms), in particular for problems on the continuum. The author gives a complete presentation of the theory of proper forcing and its relatives, starting from the beginning and avoiding the metamathematical considerations. No prior knowledge of forcing is required. The book will enable a researcher interested in an independence result of the appropriate kind to have much of the work done for them, thereby allowing them to quote general results.
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 Handbook of Set Theory written by Matthew Foreman and published by Springer Science & Business Media. This book was released on 2009-12-10 with total page 2200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numbers imitate space, which is of such a di?erent nature —Blaise Pascal It is fair to date the study of the foundation of mathematics back to the ancient Greeks. The urge to understand and systematize the mathematics of the time led Euclid to postulate axioms in an early attempt to put geometry on a ?rm footing. With roots in the Elements, the distinctive methodology of mathematics has become proof. Inevitably two questions arise: What are proofs? and What assumptions are proofs based on? The ?rst question, traditionally an internal question of the ?eld of logic, was also wrestled with in antiquity. Aristotle gave his famous syllogistic s- tems, and the Stoics had a nascent propositional logic. This study continued with ?ts and starts, through Boethius, the Arabs and the medieval logicians in Paris and London. The early germs of logic emerged in the context of philosophy and theology. The development of analytic geometry, as exempli?ed by Descartes, ill- tratedoneofthedi?cultiesinherentinfoundingmathematics. Itisclassically phrased as the question ofhow one reconciles the arithmetic with the geom- ric. Arenumbers onetypeofthingand geometricobjectsanother? Whatare the relationships between these two types of objects? How can they interact? Discovery of new types of mathematical objects, such as imaginary numbers and, much later, formal objects such as free groups and formal power series make the problem of ?nding a common playing ?eld for all of mathematics importunate. Several pressures made foundational issues urgent in the 19th century.
Download or read book Fast Track to Forcing written by Mirna Džamonja and published by Cambridge University Press. This book was released on 2020-10-15 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: This quick yet detailed introduction to set theory and forcing builds the reader's intuition about it as much as the mathematical detail. Intuition, rather absent from the existing literature on the subject, here plays a large role. The reader will not only learn the facts, but will understand why they are true and will be brought to ask: what else could be true? Having presented forcing in Part I, the second part of the book discusses contemporary issues in the theory of forcing. It includes known and some previously unpublished results as well as many open questions. This is ideal for those who want to start a research career in forcing but do not have a personal interlocutor. Obviously, not everything about forcing is in this book. Many references are included to help the reader further explore the vast amount of research literature available on the subject.
Download or read book Descriptive Set Theory and Definable Forcing written by Jindřich Zapletal and published by American Mathematical Soc.. This book was released on 2004 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on the relationship between definable forcing and descriptive set theory; the forcing serves as a tool for proving independence of inequalities between cardinal invariants of the continuum.
Download or read book Centenary of the Borel Conjecture written by Marion Scheepers and published by American Mathematical Soc.. This book was released on 2020-09-04 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Borel's Conjecture entered the mathematics arena in 1919 as an innocuous remark about sets of real numbers in the context of a new covering property introduced by Émile Borel. In the 100 years since, this conjecture has led to a remarkably rich adventure of discovery in mathematics, producing independent results and the discovery of countable support iterated forcing, developments in infinitary game theory, deep connections with infinitary Ramsey Theory, and significant impact on the study of topological groups and topological covering properties. The papers in this volume present a broad introduction to the frontiers of research that has been spurred on by Borel's 1919 conjecture and identify fundamental unanswered research problems in the field. Philosophers of science and historians of mathematics can glean from this collection some of the typical trends in the discovery, innovation, and development of mathematical theories.
Download or read book Proper Forcing written by S. Shelah and published by Springer. This book was released on 2013-12-11 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes can be viewed and used in several different ways, each has some justification, a collection of papers, a research monograph or a text book. The author has lectured variants of several of the chapters several times: in University of California, Berkeley, 1978, Ch. III , N, V in Ohio State Univer sity in Columbus, Ohio 1979, Ch. I,ll and in the Hebrew University 1979/80 Ch. I, II, III, V, and parts of VI. Moreover Azriel Levi, who has a much better name than the author in such matters, made notes from the lectures in the Hebrew University, rewrote them, and they ·are Chapters I, II and part of III , and were somewhat corrected and expanded by D. Drai, R. Grossberg and the author. Also most of XI §1-5 were lectured on and written up by Shai Ben David. Also our presentation is quite self-contained. We adopted an approach I heard from Baumgartner and may have been used by others: not proving that forcing work, rather take axiomatically that it does and go ahead to applying it. As a result we assume only knowledge of naive set theory (except some iso lated points later on in the book).
Download or read book Combinatorial Set Theory written by Lorenz J. Halbeisen and published by Springer Science & Business Media. This book was released on 2011-11-24 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lies on the axiom of choice and Ramsey theory. In the second part, the sophisticated technique of forcing, originally developed by Paul Cohen, is explained in great detail. With this technique, one can show that certain statements, like the continuum hypothesis, are neither provable nor disprovable from the axioms of set theory. In the last part, some topics of classical set theory are revisited and further developed in the light of forcing. The notes at the end of each chapter put the results in a historical context, and the numerous related results and the extensive list of references lead the reader to the frontier of research. This book will appeal to all mathematicians interested in the foundations of mathematics, but will be of particular use to graduates in this field.
Download or read book Logic and Its Applications written by Kamal Lodaya and published by Springer. This book was released on 2012-12-22 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book constitutes the refereed proceedings of the 5th Indian Conference on Logic and Its Applications, ICLA 2013, held in Chennai, India, in January 2013. The 15 revised full papers presented together with 7 invited talks were carefully reviewed and selected from numerous submissions. The papers cover the topics related to pure and applied logic, foundations and philosophy of mathematics and the sciences, set theory, model theory, proof theory, areas of theoretical computer science, artificial intelligence and other disciplines which are of direct interest to mathematical and philosophical logic.
Download or read book Featured Reviews in Mathematical Reviews 1997 1999 written by Donald G. Babbitt and published by American Mathematical Soc.. This book was released on 2000-05-05 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume of Featured Reviews makes available special detailed reviews of some of the most important mathematical articles and books published from 1997 through 1999. Also included are excellent reviews of several classic books and articles published prior to 1970. Among those reviews, for example, are the following: Homological Algebra by Henri Cartan and Samuel Eilenberg, reviewed by G. Hochschild; Faisceaux algebriques coherents by Jean-Pierre Serre, reviewed by C. Chevalley; and On the Theory of General Partial Differential Operators by Lars Hormander, reviewed by J. L. Lions. In particular, those seeking information on current developments outside their own area of expertise will find the volume very useful. By identifying some of the best publications, papers, and books that have had or are expected to have a significant impact in applied and pure mathematics, this volume will serve as a comprehensive guide to important new research across all fields covered by MR.
Download or read book Classical and New Paradigms of Computation and their Complexity Hierarchies written by Benedikt Löwe and published by Springer Science & Business Media. This book was released on 2007-11-04 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of complexity is an important contribution of logic to theoretical computer science and mathematics. This volume attempts to approach complexity in a holistic way, investigating mathematical properties of complexity hierarchies at the same time as discussing algorithms and computational properties. A main focus of the volume is on some of the new paradigms of computation, among them Quantum Computing and Infinitary Computation. The papers in the volume are tied together by an introductory article describing abstract properties of complexity hierarchies. This volume will be of great interest to both mathematical logicians and theoretical computer scientists, providing them with new insights into the various views of complexity and thus shedding new light on their own research.
Download or read book Sets and Extensions in the Twentieth Century written by and published by Elsevier. This book was released on 2012-01-24 with total page 878 pages. Available in PDF, EPUB and Kindle. Book excerpt: Set theory is an autonomous and sophisticated field of mathematics that is extremely successful at analyzing mathematical propositions and gauging their consistency strength. It is as a field of mathematics that both proceeds with its own internal questions and is capable of contextualizing over a broad range, which makes set theory an intriguing and highly distinctive subject. This handbook covers the rich history of scientific turning points in set theory, providing fresh insights and points of view. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in mathematics, the history of philosophy, and any discipline such as computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration - Serves as a singular contribution to the intellectual history of the 20th century - Contains the latest scholarly discoveries and interpretative insights
Download or read book Logic Colloquium 2007 written by Françoise Delon and published by Cambridge University Press. This book was released on 2010-06-07 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Annual European Meeting of the Association for Symbolic Logic, also known as the Logic Colloquium, is among the most prestigious annual meetings in the field. The current volume, Logic Colloquium 2007, with contributions from plenary speakers and selected special session speakers, contains both expository and research papers by some of the best logicians in the world. This volume covers many areas of contemporary logic: model theory, proof theory, set theory, and computer science, as well as philosophical logic, including tutorials on cardinal arithmetic, on Pillay's conjecture, and on automatic structures. This volume will be invaluable for experts as well as those interested in an overview of central contemporary themes in mathematical logic.
Download or read book Canonical Ramsey Theory on Polish Spaces written by Vladimir Kanovei and published by Cambridge University Press. This book was released on 2013-09-12 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lays the foundations for a new area of descriptive set theory: the connection between forcing and analytic equivalence relations.
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 2010 with total page 859 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the revised edition of a well-established monograph on the identification of a canonical model in which the Continuum Hypothesis is false. Written by an expert in the field, it is directed to researchers and advanced graduate students in Mat
Download or read book Foundations of Mathematics written by Andrés Eduardo Caicedo and published by American Mathematical Soc.. This book was released on 2017-05-12 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Logic at Harvard conference in honor of W. Hugh Woodin's 60th birthday, held March 27–29, 2015, at Harvard University. It presents a collection of papers related to the work of Woodin, who has been one of the leading figures in set theory since the early 1980s. The topics cover many of the areas central to Woodin's work, including large cardinals, determinacy, descriptive set theory and the continuum problem, as well as connections between set theory and Banach spaces, recursion theory, and philosophy, each reflecting a period of Woodin's career. Other topics covered are forcing axioms, inner model theory, the partition calculus, and the theory of ultrafilters. This volume should make a suitable introduction to Woodin's work and the concerns which motivate it. The papers should be of interest to graduate students and researchers in both mathematics and philosophy of mathematics, particularly in set theory, foundations and related areas.
