# Dense ideals and cardinal arithmetic

## TL;DR

This paper demonstrates the consistency of certain dense ideals on power sets of successor cardinals, exploring their relationship with cardinal arithmetic and combinatorial principles, and addressing open questions in the field.

## Contribution

It introduces new consistency results for dense ideals on $ ext{P}_ ext{kappa}( ext{lambda})$ derived from large cardinal assumptions, linking ideals with cardinal arithmetic and combinatorics.

## Key findings

- Proves the consistency of normal, fine, $ ext{kappa}$-complete $ ext{lambda}$-dense ideals on $ ext{P}_ ext{kappa}( ext{lambda})$ for successor $ ext{kappa}$.
- Explores the relationship between dense ideals, cardinal arithmetic, and square principles.
- Answers open questions posed by Foreman regarding dense ideals and their properties.

## Abstract

From large cardinals we show the consistency of normal, fine, $\kappa$-complete $\lambda$-dense ideals on $\mathcal{P}_\kappa(\lambda)$ for successor $\kappa$. We explore the interplay between dense ideals, cardinal arithmetic, and squares, answering some open questions of Foreman.