On what I do not understand (and have something to say): Part I

TL;DR

This paper presents a personal, informal exploration of various set theory problems, including discussions of the author's interests, attempted solutions, and anecdotes, emphasizing a subjective perspective rather than formal results.

Contribution

It offers a unique, autobiographical perspective on open problems in set theory and model theory, blending personal insights with problem discussions.

Findings

Personal insights into set theory problems

Discussion of attempted solutions and failures

Historical and contextual references

Abstract

This is a non-standard paper, containing some problems in set theory I have in various degrees been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me, sometimes the problems are presented with a discussion of how I have tried to solve them, and sometimes with failed tries, anecdote and opinion. So the discussion is quite personal, in other words, egocentric and somewhat accidental. As we discuss many problems, history and side references are erratic, usually kept at a minimum (``see ... '' means: see the references there and possibly the paper itself). The base were lectures in Rutgers Fall'97 and reflect my knowledge then. The other half, concentrating on model theory, will subsequently appear.