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Author : Lev D. Beklemishev
Publisher : Elsevier
ISBN 13 : 0080954863
Total Pages : 365 pages
Book Rating : 4.0/5 (89 download)
Download or read book Set Theory written by Lev D. Beklemishev and published by Elsevier. This book was released on 2000-04-01 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: Set Theory
Download or read book Aspects of Large Cardinals (Set Theory, Logic, Measurable, Strongly Compact, Extendible). written by and published by . This book was released on 1985 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Akihiro Kanamori
Publisher : Springer Science & Business Media
ISBN 13 : 3540888675
Total Pages : 555 pages
Book Rating : 4.5/5 (48 download)
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.
Author : Jinsei Yamaguchi
Publisher :
ISBN 13 :
Total Pages : 110 pages
Book Rating : 4.:/5 (142 download)
Download or read book Aspects of Large Cardinals written by Jinsei Yamaguchi and published by . This book was released on 1985 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Martin Zeman
Publisher : Walter de Gruyter
ISBN 13 : 3110857812
Total Pages : 385 pages
Book Rating : 4.1/5 (18 download)
Download or read book Inner Models and Large Cardinals written by Martin Zeman and published by Walter de Gruyter. This book was released on 2011-09-06 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an introduction to inner model theory, an area of set theory which is concerned with fine structural inner models reflecting large cardinal properties of the set theoretic universe. The monograph contains a detailed presentation of general fine structure theory as well as a modern approach to the construction of small core models, namely those models containing at most one strong cardinal, together with some of their applications. The final part of the book is devoted to a new approach encompassing large inner models which admit many Woodin cardinals. The exposition is self-contained and does not assume any special prerequisities, which should make the text comprehensible not only to specialists but also to advanced students in Mathematical Logic and Set Theory.
Author : Akihiro Kanamori
Publisher : Springer Science & Business Media
ISBN 13 : 3540888667
Total Pages : 554 pages
Book Rating : 4.5/5 (48 download)
Download or read book The Higher Infinite written by Akihiro Kanamori and published by Springer Science & Business Media. This book was released on 2008-11-28 with total page 554 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.
Author : Alexander S. Kechris
Publisher : Cambridge University Press
ISBN 13 : 1107182999
Total Pages : 317 pages
Book Rating : 4.1/5 (71 download)
Download or read book Large Cardinals, Determinacy and Other Topics written by Alexander S. Kechris and published by Cambridge University Press. This book was released on 2020-11-05 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: The final volume in a series of four books presenting the seminal papers from the Caltech-UCLA 'Cabal Seminar'.
Author : Frank Robert Drake
Publisher :
ISBN 13 : 9780720422009
Total Pages : 0 pages
Book Rating : 4.4/5 (22 download)
Download or read book Set Theory written by Frank Robert Drake and published by . This book was released on 1974 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Mohamed Bekkali
Publisher : Springer
ISBN 13 : 9783540541219
Total Pages : 128 pages
Book Rating : 4.5/5 (412 download)
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.
Author : Matthew Foreman
Publisher : Springer Science & Business Media
ISBN 13 : 1402057644
Total Pages : 2200 pages
Book Rating : 4.4/5 (2 download)
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.
Author : Frank R. Drake
Publisher :
ISBN 13 : 9780720422009
Total Pages : 351 pages
Book Rating : 4.4/5 (22 download)
Download or read book Set Theory written by Frank R. Drake and published by . This book was released on 1974 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ralf Schindler
Publisher : Springer
ISBN 13 : 3319067257
Total Pages : 335 pages
Book Rating : 4.3/5 (19 download)
Download or read book Set Theory written by Ralf Schindler and published by Springer. This book was released on 2014-05-22 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook gives an introduction to axiomatic set theory and examines the prominent questions that are relevant in current research in a manner that is accessible to students. Its main theme is the interplay of large cardinals, inner models, forcing and descriptive set theory. The following topics are covered: • Forcing and constructability • The Solovay-Shelah Theorem i.e. the equiconsistency of ‘every set of reals is Lebesgue measurable’ with one inaccessible cardinal • Fine structure theory and a modern approach to sharps • Jensen’s Covering Lemma • The equivalence of analytic determinacy with sharps • The theory of extenders and iteration trees • A proof of projective determinacy from Woodin cardinals. Set Theory requires only a basic knowledge of mathematical logic and will be suitable for advanced students and researchers.
Author : K. Kunen
Publisher : Elsevier
ISBN 13 : 148329515X
Total Pages : 1282 pages
Book Rating : 4.4/5 (832 download)
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.
Author : P. Erdös
Publisher : Elsevier
ISBN 13 : 0444537457
Total Pages : 349 pages
Book Rating : 4.4/5 (445 download)
Download or read book Combinatorial Set Theory: Partition Relations for Cardinals written by P. Erdös and published by Elsevier. This book was released on 2011-08-18 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents the most important combinatorial ideas in partition calculus and discusses ordinary partition relations for cardinals without the assumption of the generalized continuum hypothesis. A separate section of the book describes the main partition symbols scattered in the literature. A chapter on the applications of the combinatorial methods in partition calculus includes a section on topology with Arhangel'skii's famous result that a first countable compact Hausdorff space has cardinality, at most continuum. Several sections on set mappings are included as well as an account of recent inequalities for cardinal powers that were obtained in the wake of Silver's breakthrough result saying that the continuum hypothesis can not first fail at a singular cardinal of uncountable cofinality.
Author : Penelope Maddy
Publisher : Clarendon Press
ISBN 13 : 0191518972
Total Pages : 265 pages
Book Rating : 4.1/5 (915 download)
Download or read book Naturalism in Mathematics written by Penelope Maddy and published by Clarendon Press. This book was released on 1997-11-13 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our much-valued mathematical knowledge rests on two supports: the logic of proof and the axioms from which those proofs begin. Naturalism in Mathematics investigates the status of the latter, the fundamental assumptions of mathematics. These were once held to be self-evident, but progress in work on the foundations of mathematics, especially in set theory, has rendered that comforting notion obsolete. Given that candidates for axiomatic status cannot be proved, what sorts of considerations can be offered for or against them? That is the central question addressed in this book. One answer is that mathematics aims to describe an objective world of mathematical objects, and that axiom candidates should be judged by their truth or falsity in that world. This promising view—realism—is assessed and finally rejected in favour of another—naturalism—which attends less to metaphysical considerations of objective truth and falsity, and more to practical considerations drawn from within mathematics itself. Penelope Maddy defines this naturalism, explains the motivation for it, and shows how it can be helpfully applied in the assessment of candidates for axiomatic status in set theory. Maddy's clear, original treatment of this fundamental issue is informed by current work in both philosophy and mathematics, and will be accessible and enlightening to readers from both disciplines.
Author : William Thompson Boos
Publisher :
ISBN 13 :
Total Pages : 174 pages
Book Rating : 4.:/5 (89 download)
Download or read book Nonstandard Large Cardinals written by William Thompson Boos and published by . This book was released on 1971 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Peter J Gwyn
Publisher : Random House
ISBN 13 : 1446475131
Total Pages : 690 pages
Book Rating : 4.4/5 (464 download)
Download or read book The King's Cardinal written by Peter J Gwyn and published by Random House. This book was released on 2011-04-30 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proud, greedy, corrupt and driven by overwhelming personal ambition. Such is the traditional image of Thomas Wolsey, Lord Chancellor, Archbishop of York, Bishop of Winchester, Abbot of St. Albans, Bishop if Tournai and Papal Legate. It is an image which Peter Gwyn examines, challenges and decisively overturns in this remarkable book. From exceedingly humble beginnings Wolsey rose to a pinnacle of power unsurpassed by any other British commoner. Peter Gwyn explores every aspect of the Cardinal's career - not least his relationship with Henry VIII - and sets it firmly in a vividly recreated Tudor world. The Wolsey who emerges is a man of prodigious energy and ability, a tireless dispenser of justice, an enlightened reformer wholly dedicated to his king and country - a man who has been consistently misrepresented and maligned for four-and-a-half centuries.
