Discovering Modern Set Theory
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Author | : Winfried Just |
Publisher | : American Mathematical Soc. |
Total Pages | : 230 |
Release | : 1996 |
Genre | : Mathematics |
ISBN | : 0821802666 |
This book bridges the gap between the many elementary introductions to set theory that are available today and the more advanced, specialized monographs. The authors have taken great care to motivate concepts as they are introduced. The large number of exercises included make this book especially suitable for self-study. Students are guided towards their own discoveries in a lighthearted, yet rigorous manner.
Author | : Winfried Just |
Publisher | : American Mathematical Soc. |
Total Pages | : 232 |
Release | : |
Genre | : Mathematics |
ISBN | : 9780821872475 |
A two-volume graduate text in set theory. The first volume covers the basics of modern set theory and is addressed primarily to beginning graduate students. This second volume is intended as a bridge between introductory set theory courses and advanced monographs that cover selected branches of set theory, such as forcing or large cardinals.
Author | : Winfried Just |
Publisher | : |
Total Pages | : |
Release | : 1996 |
Genre | : Set theory |
ISBN | : |
Author | : Winfried Just |
Publisher | : American Mathematical Soc. |
Total Pages | : 240 |
Release | : 1996 |
Genre | : Mathematics |
ISBN | : 0821805282 |
This is the second volume of a two-volume graduate text in set theory. The first volume covered the basics of modern set theory and was addressed primarily to beginning graduate students. The second volume is intended as a bridge between introductory set theory courses such as the first volume and advanced monographs that cover selected branches of set theory. The authors give short but rigorous introductions to set-theoretic concepts and techniques such as trees, partition calculus, cardinal invariants of the continuum, Martin's Axiom, closed unbounded and stationary sets, the Diamond Principle, and the use of elementary submodels. Great care is taken to motivate concepts and theorems presented.
Author | : Winfried Just and Martin Weese |
Publisher | : American Mathematical Soc. |
Total Pages | : 244 |
Release | : |
Genre | : Set theory |
ISBN | : 9780821872086 |
Author | : Winfried Just |
Publisher | : |
Total Pages | : |
Release | : 1996 |
Genre | : Set theory |
ISBN | : |
Author | : Ralf Schindler |
Publisher | : Springer |
Total Pages | : 335 |
Release | : 2014-05-22 |
Genre | : Mathematics |
ISBN | : 3319067257 |
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 | : Judith Roitman |
Publisher | : John Wiley & Sons |
Total Pages | : 188 |
Release | : 1990-01-16 |
Genre | : Mathematics |
ISBN | : 9780471635192 |
This is modern set theory from the ground up--from partial orderings and well-ordered sets to models, infinite cobinatorics and large cardinals. The approach is unique, providing rigorous treatment of basic set-theoretic methods, while integrating advanced material such as independence results, throughout. The presentation incorporates much interesting historical material and no background in mathematical logic is assumed. Treatment is self-contained, featuring theorem proofs supported by diagrams, examples and exercises. Includes applications of set theory to other branches of mathematics.
Author | : Winfried Just |
Publisher | : |
Total Pages | : 224 |
Release | : 1997 |
Genre | : |
ISBN | : |
Author | : Yiannis N. Moschovakis |
Publisher | : American Mathematical Soc. |
Total Pages | : 521 |
Release | : 2009-06-30 |
Genre | : Mathematics |
ISBN | : 0821848135 |
Descriptive Set Theory is the study of sets in separable, complete metric spaces that can be defined (or constructed), and so can be expected to have special properties not enjoyed by arbitrary pointsets. This subject was started by the French analysts at the turn of the 20th century, most prominently Lebesgue, and, initially, was concerned primarily with establishing regularity properties of Borel and Lebesgue measurable functions, and analytic, coanalytic, and projective sets. Its rapid development came to a halt in the late 1930s, primarily because it bumped against problems which were independent of classical axiomatic set theory. The field became very active again in the 1960s, with the introduction of strong set-theoretic hypotheses and methods from logic (especially recursion theory), which revolutionized it. This monograph develops Descriptive Set Theory systematically, from its classical roots to the modern ``effective'' theory and the consequences of strong (especially determinacy) hypotheses. The book emphasizes the foundations of the subject, and it sets the stage for the dramatic results (established since the 1980s) relating large cardinals and determinacy or allowing applications of Descriptive Set Theory to classical mathematics. The book includes all the necessary background from (advanced) set theory, logic and recursion theory.