Cardinal Sequences Of Pcf Structures

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Cardinal Sequences Of Pcf Structures

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Author : Jonathan Conrad Ruyle
language : en
Publisher:
Release Date : 1999

Cardinal Sequences Of Pcf Structures written by Jonathan Conrad Ruyle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Cardinal numbers categories.

Combinatorics Of Singular Cardinals And Pcf Structures

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Author : Luis Miguel Da Silva Pereira
language : en
Publisher:
Release Date : 2007

Combinatorics Of Singular Cardinals And Pcf Structures written by Luis Miguel Da Silva Pereira and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.

This work is centered on Shelah's PCF theory. We study the connection between the topology of PCF spaces and standard PCF theory notions. We prove a generalization of the result that says that separable PCF spaces are sequential and obtain as a corollary that there exist many sequences that have true cofinality modulo the ideal of finite sets. We prove that this corollary is optimal. We also give a topological proof of cardinal estimates previously obtained through the use of the Galvin-Hajnal norm. We study a consequence of the negation of Shelah's PCF conjecture called the Approachable Free Subset Property (AFSP). We note that AFSP is incompatible with the existence of tree-like continuous scales and prove the consistency of these scales with the largest large cardinal axioms thus establishing that AFSP is not implied by large cardinals. We study the existence of tree-like continuous scales and the negation of AFSP in several Prikry extensions of the universe.

Open Problems In Topology Ii

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Author : Elliott M. Pearl
language : en
Publisher: Elsevier
Release Date : 2011-08-11

Open Problems In Topology Ii written by Elliott M. Pearl and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-11 with Mathematics categories.

This volume is a collection of surveys of research problems in topology and its applications. The topics covered include general topology, set-theoretic topology, continuum theory, topological algebra, dynamical systems, computational topology and functional analysis. * New surveys of research problems in topology * New perspectives on classic problems * Representative surveys of research groups from all around the world

Introduction To Cardinal Arithmetic

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Author : Michael Holz
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-11-23

Introduction To Cardinal Arithmetic written by Michael Holz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-11-23 with Mathematics categories.

This book is an introduction to modern cardinal arithmetic, developed in the frame of the axioms of Zermelo-Fraenkel set theory together with the axiom of choice. It splits into three parts. Part one, which is contained in Chapter 1, describes the classical cardinal arithmetic due to Bernstein, Cantor, Hausdorff, Konig, and Tarski. The results were found in the years between 1870 and 1930. Part two, which is Chapter 2, characterizes the development of cardinal arith metic in the seventies, which was led by Galvin, Hajnal, and Silver. The third part, contained in Chapters 3 to 9, presents the fundamental investigations in pcf-theory which has been developed by S. Shelah to answer the questions left open in the seventies. All theorems presented in Chapter 3 and Chapters 5 to 9 are due to Shelah, unless otherwise stated. We are greatly indebted to all those set theorists whose work we have tried to expound. Concerning the literature we owe very much to S. Shelah's book [Sh5] and to the article by M. R. Burke and M. Magidor [BM] which also initiated our students' interest for Shelah's pcf-theory.

Dissertation Abstracts International

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Author :
language : en
Publisher:
Release Date : 1999

Dissertation Abstracts International written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Dissertations, Academic categories.

Cardinal Arithmetic

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Author : Saharon Shelah
language : en
Publisher: Oxford University Press on Demand
Release Date : 1994

Cardinal Arithmetic written by Saharon Shelah and has been published by Oxford University Press on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.

Is the continuum hypothesis still open? If we interpret it as finding the laws of cardinal arithmetic (really exponentiation since addition and multiplication were classically solved), it was thought to be essentially solved by the independence results of Godel and Cohen (and Easton) with some isolated positive results (likeGalvin-Hajnal). It was expected that only more independence results remained to be proved. The author has come to change his view. This enables us to get new results for the conventional cardinal arithmetic, thus supporting the interest in our view. We also find other applications, extend older methods of using normal fiters and prove the existence of Jonsson algebra.

Self Similarity At Singular Cardinals

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Author : Andreas Jue-der Liu
language : en
Publisher:
Release Date : 2004

Self Similarity At Singular Cardinals written by Andreas Jue-der Liu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.

Set Theory

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Author : Simon Thomas
language : en
Publisher: American Mathematical Soc.
Release Date : 2002

Set Theory written by Simon Thomas and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

This volume presents the proceedings from the Mid-Atlantic Mathematical Logic Seminar (MAMLS) conference held in honor of Andras Hajnal at the DIMACS Center, Rutgers University (New Brunswick, NJ). Articles include both surveys and high-level research papers written by internationally recognized experts in the field of set theory. Many of the current active areas of set theory are represented in this volume. It includes research papers on combinatorial set theory, set theoretictopology, descriptive set theory, and set theoretic algebra. There are valuable surveys on combinatorial set theory, fragments of the proper forcing axiom, and the reflection properties of stationary sets. The book also includes an exposition of the ergodic theory of lattices in higher rank semisimpleLie groups-essential reading for anyone who wishes to understand much of the recent work on countable Borel equivalence relations.

Logic Colloquium 2007

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Author : Françoise Delon
language : en
Publisher: Cambridge University Press
Release Date : 2010-06-07

Logic Colloquium 2007 written by Françoise Delon and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-07 with Mathematics categories.

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.

Handbook Of Set Theory

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Author : Matthew Foreman
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-10

Handbook Of Set Theory written by Matthew Foreman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-10 with Mathematics categories.

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.