Canonical Ramsey Theory on Polish Spaces
Nonfiction, Science & Nature, Mathematics, Set Theory, Logic
| Author: | Vladimir Kanovei, Marcin Sabok, Jindřich Zapletal | ISBN: | 9781107424234 |
| Publisher: | Cambridge University Press | Publication: | September 12, 2013 |
| Imprint: | Cambridge University Press | Language: | English |
| Author: | Vladimir Kanovei, Marcin Sabok, Jindřich Zapletal |
| ISBN: | 9781107424234 |
| Publisher: | Cambridge University Press |
| Publication: | September 12, 2013 |
| Imprint: | Cambridge University Press |
| Language: | English |
This book lays the foundations for an exciting new area of research in descriptive set theory. It develops a robust connection between two active topics: forcing and analytic equivalence relations. This in turn allows the authors to develop a generalization of classical Ramsey theory. Given an analytic equivalence relation on a Polish space, can one find a large subset of the space on which it has a simple form? The book provides many positive and negative general answers to this question. The proofs feature proper forcing and Gandy–Harrington forcing, as well as partition arguments. The results include strong canonization theorems for many classes of equivalence relations and sigma-ideals, as well as ergodicity results in cases where canonization theorems are impossible to achieve. Ideal for graduate students and researchers in set theory, the book provides a useful springboard for further research.
This book lays the foundations for an exciting new area of research in descriptive set theory. It develops a robust connection between two active topics: forcing and analytic equivalence relations. This in turn allows the authors to develop a generalization of classical Ramsey theory. Given an analytic equivalence relation on a Polish space, can one find a large subset of the space on which it has a simple form? The book provides many positive and negative general answers to this question. The proofs feature proper forcing and Gandy–Harrington forcing, as well as partition arguments. The results include strong canonization theorems for many classes of equivalence relations and sigma-ideals, as well as ergodicity results in cases where canonization theorems are impossible to achieve. Ideal for graduate students and researchers in set theory, the book provides a useful springboard for further research.
