On what I do not understand (and have something to say), model theory

TL;DR

This paper presents a personal, informal exploration of various open problems in model theory, including discussions on their significance, attempted solutions, and the author's perspectives, reflecting a non-standard, anecdotal approach.

Contribution

It offers a unique, subjective collection of problems and insights in model theory, blending personal commentary with mathematical discussion, diverging from traditional formal expositions.

Findings

Discusses open problems in model theory

Shares personal insights and attempted solutions

Highlights the subjective nature of mathematical exploration

Abstract

This is a non-standard paper, containing some problems, mainly in model theory, which 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, math.LO/9906113, concentrating on set theory, is in print, but the two halves are independent. We thank A. Blass, G. Cherlin and R. Grossberg for some corrections.