Simplified Independence Proofs
Author | : |
Publisher | : Academic Press |
Total Pages | : 237 |
Release | : 2011-08-29 |
Genre | : Mathematics |
ISBN | : 008087343X |
Simplified Independence Proofs
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Author | : |
Publisher | : Academic Press |
Total Pages | : 237 |
Release | : 2011-08-29 |
Genre | : Mathematics |
ISBN | : 008087343X |
Simplified Independence Proofs
Author | : K. Kunen |
Publisher | : Elsevier |
Total Pages | : 330 |
Release | : 2014-06-28 |
Genre | : Mathematics |
ISBN | : 0080570585 |
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.
Author | : Martin Aigner |
Publisher | : Springer Science & Business Media |
Total Pages | : 194 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 3662223430 |
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
Author | : G. Menges |
Publisher | : Springer Science & Business Media |
Total Pages | : 196 |
Release | : 2012-12-06 |
Genre | : Social Science |
ISBN | : 9401021597 |
Under the title 'Information, Inference and Decision' this volume in the Theory and Decision Library presents some papers on issues from the borderland of statistical inference philosophy and epistemology, written by statisticians and decision theorists who belonged or are allied to the former Saarbriicken school of statistical decision theory. In the first part I make an attempt to outline an objective theory of inductive behaviour, on the basis of R. A. Fisher's statistical inference philosophy, on the one hand, and R. Carnap's inductive logic, on the other. A special problem arising in the context of the new theory, viz., the problem of vagueness of concepts (in particular in the social sciences) is treated separately by H. Skala and myself. B. Leiner has contributed some biographical and bibliographical notes on the objective theory of inductive behaviour. Part II is concerned with inference philosophy. D. A. S. Fraser, the founder of structural inference theory, characterizes and compares some inference philosophies, and discusses his own and the arguments of the critics of his structural theory. In my opinion, Fraser's structural infer ence theory is suited to complete Fisher's inference philosophy in some essential points, if not to replace it. An interesting task for future re search work is to establish the connection between Fraser's theory and Carnap's ideas in the framework of an objective theory of inductive behaviour.
Author | : Akihiro Kanamori |
Publisher | : Springer Science & Business Media |
Total Pages | : 555 |
Release | : 2008-11-23 |
Genre | : Mathematics |
ISBN | : 3540888675 |
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 | : D.C. Goldrei |
Publisher | : Routledge |
Total Pages | : 300 |
Release | : 2017-09-06 |
Genre | : Mathematics |
ISBN | : 1351460609 |
Designed for undergraduate students of set theory, Classic Set Theory presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. This includes:The definition of the real numbers in terms of rational numbers and ultimately in terms of natural numbersDefining natural numbers in terms of setsThe potential paradoxes in set theoryThe Zermelo-Fraenkel axioms for set theoryThe axiom of choiceThe arithmetic of ordered setsCantor's two sorts of transfinite number - cardinals and ordinals - and the arithmetic of these.The book is designed for students studying on their own, without access to lecturers and other reading, along the lines of the internationally renowned courses produced by the Open University. There are thus a large number of exercises within the main body of the text designed to help students engage with the subject, many of which have full teaching solutions. In addition, there are a number of exercises without answers so students studying under the guidance of a tutor may be assessed.Classic Set Theory gives students sufficient grounding in a rigorous approach to the revolutionary results of set theory as well as pleasure in being able to tackle significant problems that arise from the theory.
Author | : Paul R. Halmos |
Publisher | : American Mathematical Soc. |
Total Pages | : 348 |
Release | : 1999-04-27 |
Genre | : Mathematics |
ISBN | : 9780821886090 |
Paul R. Halmos, eminent mathematician, is also a snapshot addict. For the past 45 years, Halmos has snapped mathematicians, their spouses, their brothers and sisters and other relatives, their offices, their dogs, and their carillon towers. From 6000 or so photographs in his collection, Halmos chose about 600 for this book. The pictures are candid shots showing mathematicians just being themselves, and the accompanying captions, in addition to identifying the subjects, contain anecdotes and bits of history that reveal Halmos' inimitable wit and insight.
Author | : David DeVidi |
Publisher | : Springer Science & Business Media |
Total Pages | : 487 |
Release | : 2011-03-23 |
Genre | : Philosophy |
ISBN | : 9400702140 |
The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bell’s own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic (William Lawvere, Peter Aczel, Graham Priest, Giovanni Sambin); analytical philosophy (Michael Dummett, William Demopoulos), philosophy of science (Michael Redhead, Frank Arntzenius), philosophy of mathematics (Michael Hallett, John Mayberry, Daniel Isaacson) and decision theory and foundations of economics (Ken Bimore). Most articles are contributions to current philosophical debates, but contributions also include some new mathematical results, important historical surveys, and a translation by Wilfrid Hodges of a key work of arabic logic.
Author | : U. Felgner |
Publisher | : Springer |
Total Pages | : 179 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540369082 |