Linearization of partial quasi-orderings in the Solovay model revisited

TL;DR

This paper revisits and modifies existing arguments to reprove a theorem on linearizing certain definable orderings within the Solovay model, enhancing understanding of definable quasi-orders.

Contribution

It provides a new proof of a linearization theorem for real-ordinal definable partial quasi-orderings in the Solovay model, refining previous methods.

Findings

Reproves a linearization theorem in the Solovay model

Adapts existing arguments for definable orderings

Enhances understanding of definable quasi-orders in set theory

Abstract

We modify arguments in Vladimir Kanovei, Linearization of definable order relations, APAL, 102(1-2):69--100, 2000, to reprove a linearization theorem on real-ordinal definable partial quasi-orderings in the Solovay model.