Tiltan

TL;DR

This paper explores the consistency of tiltan with various set-theoretic properties, demonstrating its compatibility with negations and large cardinal assumptions, and contrasting it with superclub's implications.

Contribution

It establishes the consistency of tiltan with the negation of Galvin's property and large splitting numbers at supercompact cardinals, expanding understanding of tiltan's set-theoretic implications.

Findings

Tiltan is consistent with the negation of Galvin's property.

Superclub implies Galvin's property.

Tiltan is consistent with a large splitting number at a supercompact cardinal.

Abstract

We prove that tiltan is consistent with the negation of Galvin's property. On the other hand, superclub implies Galvin's property. We also show that tiltan is consistent with a large value of the splitting number at kappa, where kappa is supercompact.