On the diamenter of Lascar strong types (after Ludomir Newelski)

TL;DR

This paper provides an exposition of a theorem in mathematical logic demonstrating that type-definable Lascar strong types have finite diameter, based on a proof involving structure, elementary equivalence, and compactness.

Contribution

It offers a new exposition of Newelski's theorem, replacing the notion of weak c-free with the introduced concept of non-drifting.

Findings

Type-definable Lascar strong types have finite diameter.

The proof relies on structure, elementary equivalence, and compactness.

The exposition introduces the concept of non-drifting as a key notion.

Abstract

This is an exposition a theorem of mathematical logic which only assumes the notions of structure, elementary equivalence, and compactness (saturation). Newelski proved that type-definable Lascar strong types have finite diameter. Our exposition is based on a proof that appears in Pelaez' thesis - up to a minor difference: the notion of weak c-free is replaced with the notion of non-drifting that is introduced here.