Proof theory of weak compactness

TL;DR

This paper explores the proof-theoretic foundations of weakly compact cardinals, demonstrating their reducibility to specific set-theoretic operations within Zermelo-Fraenkel set theory.

Contribution

It establishes a proof-theoretic reduction of weakly compact cardinals to iterations of Mostowski collapsings and Mahlo operations.

Findings

Weakly compact cardinals are proof-theoretically reducible to set-theoretic operations.

The reduction involves iterations of Mostowski collapsings and Mahlo operations.

This links large cardinal axioms to concrete proof-theoretic procedures.

Abstract

We show that the existence of a weakly compact cardinal over the Zermelo-Fraenkel's set theory is proof-theoretically reducible to iterations of Mostowski collapsings and Mahlo operations.