Magidor-Malitz Reflection

TL;DR

This paper explores the implications of extending first-order logic with the Magidor-Malitz quantifier, focusing on the downward Löwenheim-Skolem theorem, combinatorial results, and bounds related to Chang's Conjecture.

Contribution

It provides new insights into the consistency and consequences of Magidor-Malitz logic extensions, including improved bounds for Chang's Conjecture at certain cardinals.

Findings

Derived combinatorial results related to the logic extension.

Improved upper bounds for the consistency of Chang's Conjecture.

Analyzed the consequences of the downward Löwenheim-Skolem theorem for Magidor-Malitz logic.

Abstract

In this paper we investigate the consequences and consistency of the downward L\"owenheim-Skolem theorem for extension of the first order logic by the Magidor-Malitz quantifier. We derive some combinatorial results and improve the known upper bound for the consistency of Chang's Conjecture at successor of singular cardinals.