The Size Of Maximal Almost Disjoint Families
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Descriptive Set Theory And Definable Forcing
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Author : Jindřich Zapletal
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Descriptive Set Theory And Definable Forcing written by Jindřich Zapletal 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 2004 with Mathematics categories.
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.
Surveys In Combinatorics 1987
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Author : C. Whitehead
language : en
Publisher: CUP Archive
Release Date : 1987-07-16
Surveys In Combinatorics 1987 written by C. Whitehead and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-07-16 with Mathematics categories.
The Size Of Maximal Almost Disjoint Families
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Author : James Donald Monk
language : en
Publisher:
Release Date : 2006
The Size Of Maximal Almost Disjoint Families written by James Donald Monk and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Combinatorial set theory categories.
Size Of Maximal Almost Disjoint Families
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Author : J. D. Monk
language : pl
Publisher:
Release Date : 2006
Size Of Maximal Almost Disjoint Families written by J. D. Monk and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
Set Theory
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Author : Thomas Jech
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-05-23
Set Theory written by Thomas Jech 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 2007-05-23 with Mathematics categories.
Set Theory has experienced a rapid development in recent years, with major advances in forcing, inner models, large cardinals and descriptive set theory. The present book covers each of these areas, giving the reader an understanding of the ideas involved. It can be used for introductory students and is broad and deep enough to bring the reader near the boundaries of current research. Students and researchers in the field will find the book invaluable both as a study material and as a desktop reference.
Classical And New Paradigms Of Computation And Their Complexity Hierarchies
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Author : Benedikt Löwe
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-04
Classical And New Paradigms Of Computation And Their Complexity Hierarchies written by Benedikt Löwe 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 2007-11-04 with Computers categories.
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.
Set Theory
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Author : Abhijit Dasgupta
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
Set Theory written by Abhijit Dasgupta 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 2013-12-11 with Mathematics categories.
What is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenth-century mathematicians such as Dedekind and Cantor gave birth to set theory. This textbook presents classical set theory in an intuitive but concrete manner. To allow flexibility of topic selection in courses, the book is organized into four relatively independent parts with distinct mathematical flavors. Part I begins with the Dedekind–Peano axioms and ends with the construction of the real numbers. The core Cantor–Dedekind theory of cardinals, orders, and ordinals appears in Part II. Part III focuses on the real continuum. Finally, foundational issues and formal axioms are introduced in Part IV. Each part ends with a postscript chapter discussing topics beyond the scope of the main text, ranging from philosophical remarks to glimpses into landmark results of modern set theory such as the resolution of Lusin's problems on projective sets using determinacy of infinite games and large cardinals. Separating the metamathematical issues into an optional fourth part at the end makes this textbook suitable for students interested in any field of mathematics, not just for those planning to specialize in logic or foundations. There is enough material in the text for a year-long course at the upper-undergraduate level. For shorter one-semester or one-quarter courses, a variety of arrangements of topics are possible. The book will be a useful resource for both experts working in a relevant or adjacent area and beginners wanting to learn set theory via self-study.
Questions And Answers In General Topology
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Author :
language : en
Publisher:
Release Date : 1997
Questions And Answers In General Topology written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Topology categories.
Set Theory An Introduction To Independence Proofs
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Author : K. Kunen
language : en
Publisher: Elsevier
Release Date : 2014-06-28
Set Theory An Introduction To Independence Proofs written by K. Kunen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.
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.
Combinatorial Set Theory
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Author : Lorenz J. Halbeisen
language : en
Publisher: Springer Nature
Release Date : 2025-05-26
Combinatorial Set Theory written by Lorenz J. Halbeisen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-26 with Mathematics categories.
This book, now in a revised and extended third edition, provides a comprehensive and accessible introduction to modern axiomatic set theory. After an overview of basic notions in combinatorics and first-order logic, and discussing in great detail the axioms of set theory, the author outlines in the second part the main topics of classical set theory, including Ramsey theory and the axiom of choice. As an application of the axiom of choice, a complete proof of Robinson's construction for doubling a ball by dividing it into only five parts is given. For the new edition, the chapter on permutation models has been extended, and recent results in set theory without the axiom of choice and about cardinal characteristics have been added. The third part explains the sophisticated technique of forcing from scratch, now including more details about iterated forcing. The technique is then used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In particular, it is shown that both Martin's Axiom and Suslin's Hypothesis are independent of the axioms of set theory. The final part, with a new chapter on Laver forcing, is mainly concerned with consistency results obtained by iterations of forcing notions such as Cohen forcing, Sacks forcing, and Mathias forcing. The part begins with an extended chapter on countable support iterations of proper forcing notions, now also including proofs of some preservation theorems such as preservation of properness and of certain ultrafilters. In the following chapters, various consistency results concerning possible relations between cardinal characteristics and the existence of Ramsey ultrafilters are presented. For example, a detailed proof of Shelah’s astonishing construction of a model with finitely many Ramsey ultrafilters is given. 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, historical remarks, and related results at the end of the chapters, this book is also suitable for self-study.