MS-measurability via Coordinatization

TL;DR

This paper introduces a coordinatization framework for countably categorical structures, demonstrating that structures strongly coordinatized by MS-measurable structures inherit MS-measurability, thus linking structural expansion with measure-theoretic properties.

Contribution

It defines a new notion of coordinatization for countably categorical structures and proves that strong coordinatization by MS-measurable structures ensures MS-measurability of the entire structure.

Findings

Coordinatization concept for $eth_0$-categorical structures.

MS-measurability is preserved under strong coordinatization.

Establishes a connection between structural expansion and measure-theoretic properties.

Abstract

We define a notion of coordinatization for $\aleph_0$-categorical structures which is, like Lie coordinatized structures in [2], a certain kind of expansion of a tree. We show that a structure which is coordinatized, in a certain strong sense, by $\aleph_0$-categorical MS-measurable structures itself is MS-measurable.