| Softcover ISBN: | 978-1-4704-5462-3 |
| Product Code: | SURV/248 |
| List Price: | $140.00 |
| MAA Member Price: | $126.00 |
| AMS Member Price: | $112.00 |
| eBook ISBN: | 978-1-4704-6018-1 |
| Product Code: | SURV/248.E |
| List Price: | $140.00 |
| MAA Member Price: | $126.00 |
| AMS Member Price: | $112.00 |
| Softcover ISBN: | 978-1-4704-5462-3 |
| eBook: ISBN: | 978-1-4704-6018-1 |
| Product Code: | SURV/248.B |
| List Price: | $280.00 $210.00 |
| MAA Member Price: | $252.00 $189.00 |
| AMS Member Price: | $224.00 $168.00 |
| Softcover ISBN: | 978-1-4704-5462-3 |
| Product Code: | SURV/248 |
| List Price: | $140.00 |
| MAA Member Price: | $126.00 |
| AMS Member Price: | $112.00 |
| eBook ISBN: | 978-1-4704-6018-1 |
| Product Code: | SURV/248.E |
| List Price: | $140.00 |
| MAA Member Price: | $126.00 |
| AMS Member Price: | $112.00 |
| Softcover ISBN: | 978-1-4704-5462-3 |
| eBook ISBN: | 978-1-4704-6018-1 |
| Product Code: | SURV/248.B |
| List Price: | $280.00 $210.00 |
| MAA Member Price: | $252.00 $189.00 |
| AMS Member Price: | $224.00 $168.00 |
-
Book DetailsMathematical Surveys and MonographsVolume: 248; 2020; 330 ppMSC: Primary 03; 05; 11; 37
This book introduces a new research direction in set theory: the study of models of set theory with respect to their extensional overlap or disagreement. In Part I, the method is applied to isolate new distinctions between Borel equivalence relations. Part II contains applications to independence results in Zermelo–Fraenkel set theory without Axiom of Choice.
The method makes it possible to classify in great detail various paradoxical objects obtained using the Axiom of Choice; the classifying criterion is a ZF-provable implication between the existence of such objects. The book considers a broad spectrum of objects from analysis, algebra, and combinatorics: ultrafilters, Hamel bases, transcendence bases, colorings of Borel graphs, discontinuous homomorphisms between Polish groups, and many more. The topic is nearly inexhaustible in its variety, and many directions invite further investigation.
ReadershipGraduate students and researchers interested in current research in axiomatic set theory.
-
Table of Contents
-
Chapters
-
Introduction
-
Equivalence relations
-
The virtual realm
-
Turbulence
-
Nested sequences of models
-
Balanced extensions of the Solovay model
-
Balanced Suslin forcing
-
Simplicial complex forcings
-
Ultrafilter forcings
-
Other forcings
-
Preserving cardinalities
-
Uniformization
-
Locally countable structures
-
The Silver divide
-
The arity divide
-
Other combinatorics
-
-
Additional Material
-
RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
This book introduces a new research direction in set theory: the study of models of set theory with respect to their extensional overlap or disagreement. In Part I, the method is applied to isolate new distinctions between Borel equivalence relations. Part II contains applications to independence results in Zermelo–Fraenkel set theory without Axiom of Choice.
The method makes it possible to classify in great detail various paradoxical objects obtained using the Axiom of Choice; the classifying criterion is a ZF-provable implication between the existence of such objects. The book considers a broad spectrum of objects from analysis, algebra, and combinatorics: ultrafilters, Hamel bases, transcendence bases, colorings of Borel graphs, discontinuous homomorphisms between Polish groups, and many more. The topic is nearly inexhaustible in its variety, and many directions invite further investigation.
Graduate students and researchers interested in current research in axiomatic set theory.
-
Chapters
-
Introduction
-
Equivalence relations
-
The virtual realm
-
Turbulence
-
Nested sequences of models
-
Balanced extensions of the Solovay model
-
Balanced Suslin forcing
-
Simplicial complex forcings
-
Ultrafilter forcings
-
Other forcings
-
Preserving cardinalities
-
Uniformization
-
Locally countable structures
-
The Silver divide
-
The arity divide
-
Other combinatorics
