Classical Descriptive Set Theory / by Alexander Kechris.

Format:

Book

Author/Creator:

Kechris, A. S., 1946- Author.

Series:

Graduate Texts in Mathematics, 2197-5612 ; 156

Language:

English

Subjects (All):

Logic, Symbolic and mathematical.

Topology.

Mathematical Logic and Foundations.

Local Subjects:

Mathematical Logic and Foundations.

Topology.

Physical Description:

1 online resource (XVIII, 404 p.)

Edition:

1st ed. 1995.

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 1995.

Language Note:

English

Summary:

Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text attempts to present a largely balanced approach, which combines many elements of the different traditions of the subject. It includes a wide variety of examples, exercises (over 400), and applications, in order to illustrate the general concepts and results of the theory. This text provides a first basic course in classical descriptive set theory and covers material with which mathematicians interested in the subject for its own sake or those that wish to use it in their field should be familiar. Over the years, researchers in diverse areas of mathematics, such as logic and set theory, analysis, topology, probability theory, etc., have brought to the subject of descriptive set theory their own intuitions, concepts, terminology and notation.

Contents:

I Polish Spaces

1. Topological and Metric Spaces

2. Trees

3. Polish Spaces

4. Compact Metrizable Spaces

5. Locally Compact Spaces

6. Perfect Polish Spaces

7.Zero-dimensional Spaces

8. Baire Category

9. Polish Groups

II Borel Sets

10. Measurable Spaces and Functions

11. Borel Sets and Functions

12. Standard Borel Spaces

13. Borel Sets as Clopen Sets

14. Analytic Sets and the Separation Theorem

15. Borel Injections and Isomorphisms

16. Borel Sets and Baire Category

17. Borel Sets and Measures

18. Uniformization Theorems

19. Partition Theorems

20. Borel Determinacy

21. Games People Play

22. The Borel Hierarchy

23. Some Examples

24. The Baire Hierarchy

III Analytic Sets

25. Representations of Analytic Sets

26. Universal and Complete Sets

27. Examples

28. Separation Theorems

29. Regularity Properties

30. Capacities

31. Analytic Well-founded Relations

IV Co-Analytic Sets

32. Review

33. Examples

34. Co-Analytic Ranks

35. Rank Theory

36. Scales and Uniformiiatiou

V Projective Sets

37. The Projective Hierarchy

38. Projective Determinacy

39. The Periodicity Theorems

40. Epilogue

Appendix A. Ordinals and Cardinals

Appendix B. Well-founded Relations

Appendix C. On Logical Notation

Notes and Hints

References

Symbols and Abbreviations.

Notes:

"With 34 illustrations."

Includes bibliographical references and index.

ISBN:

1-4612-4190-1