Gentle Introduction to Descriptive Set theory

Question

If find the common literature on Descriptive Set theory pretty tough. Is there a gentle recommandation? I would really like to learn this topic on my own, so I am searching for something diguestible where the exercises are not as tough, to make progress and get the ability to read more advanced literature.

Thanks in advance.

You consider this gentle? Most of the Proofs are more or less scetches, and the easiest exercises in the book are the toughest on a homework sheet. — MrSnake, Nov 08 '21 at 10:56
Yes it is gentle. In addition, the author is one of the best in this area of math which is a big plus. — markvs, Nov 08 '21 at 11:09
I disagree with you. It is a good book, but very dense, and the exercises are pretty hard. — MrSnake, Nov 08 '21 at 11:17
A bit more basic and accessible, especially regarding background in other mathematical fields, is A Course on Borel Sets by Sashi Mohan Srivastava (1998) and Set Theory. With an Introduction to Descriptive Set Theory by Kuratowski/Mostowski (2nd edition, 1978). A lot more basic, but also of possible interest, is Set Theory by Abhijit Dasgupta (2014). (continued) — Dave L. Renfro, Nov 08 '21 at 11:48
For basics about the Borel set hierarchy and Baire function hierarchy from a real analysis perspective, see this answer and this answer. — Dave L. Renfro, Nov 08 '21 at 11:53
While I agree with the comments above that Kechris is the best book to learn DST from, there are some lecture notes by Anush Tserunyan that are based on (parts of) Kechris and are very good. They are freely available on her website, together with some exercises to go with them https://www.math.mcgill.ca/atserunyan/lecture_notes.html — Alessandro Codenotti, Nov 08 '21 at 13:58

score 4 · Answer 1 · answered Nov 08 '21 at 13:24

4

I like Chapter 8 in

Cohn, Donald L., Measure theory., Boston, MA: Birkhäuser. ix, 373 p. (1993). ZBL0860.28001.

Intended as a first course in measure theory, aimed at a student with no special knowledge of (logic, foundations, set theory).

answered Nov 08 '21 at 13:24

GEdgar

111,679

1

Thanks for the recommandation. I will take a look at it. – MrSnake Nov 08 '21 at 19:13

Gentle Introduction to Descriptive Set theory

1 Answers1