Bounding and decomposing thin analytic partial orderings

TL;DR

This paper revisits and extends foundational results on Borel orderings by modifying previous arguments to better understand the structure and decomposition of analytic subsets within Borel partial quasi-orderings.

Contribution

It introduces new modifications to existing proofs, enhancing the understanding of bounding and decomposing thin analytic partial orderings.

Findings

Extended key results on Borel orderings.

Provided new methods for bounding analytic subsets.

Improved decomposition techniques for partial orderings.

Abstract

We modify arguments by Harrington, Marker, and Shelah, 1990, to reprove extensions of two key results in their paper "Borel orderings"in the context of bounding and decomposition of analytic subsets of Borel partial quasi-orderings.