The Harrington-Shelah Model with Large Continuum

TL;DR

This paper proves the consistency of a set-theoretic model where the continuum is large, specifically $2^ ext{omega} = ext{omega}_3$, and stationary sets reflect to smaller ordinals, assuming a Mahlo cardinal.

Contribution

It establishes the consistency of a Harrington-Shelah type model with a large continuum and stationary reflection properties from a Mahlo cardinal.

Findings

Consistency of $2^ ext{omega} = ext{omega}_3$ proven.

Stationary subsets of $ ext{omega}_2$ reflect to smaller ordinals.

Assumption of a Mahlo cardinal is used for the proof.

Abstract

We prove from the existence of a Mahlo cardinal the consistency of the statement that $2^\omega = \omega_3$ holds and every stationary subset of $\omega_2 \cap \mathrm{cof}(\omega)$ reflects to an ordinal less than $\omega_2$ with cofinality $\omega_1$.