On the sepration of regularity properties of the reals

TL;DR

This paper constructs a model demonstrating the separation of various regularity properties of the real line, showing that some sets can have Silver measurability while lacking Miller and Lebesgue measurability.

Contribution

It introduces a new model where  is inaccessible by reals and different regularity properties are separated, advancing the understanding of regularity notions in set theory.

Findings

Silver measurability holds for all sets

Miller and Lebesgue measurability fail for some sets

 is inaccessible by reals in the model

Abstract

We present a model where \omega_1 is inaccessible by reals, Silver measurability holds for all sets but Miller and Lebesgue measurability fail for some sets. This contributes to a line of research started by Shelah in the 1980s and more recently continued by Schrittesser and Friedman, regarding the separation of different notions of regularity properties of the real line.