# A short mathematical proof of Frankiewicz - Kunen theorem

## TL;DR

This paper provides a direct mathematical proof that the existence of precipitous ideals follows from Kuratowski partitions, avoiding complex metamathematical methods.

## Contribution

It offers a straightforward proof linking precipitous ideals to Kuratowski partitions, simplifying previous approaches.

## Key findings

- Precipitous ideals follow from Kuratowski partitions.
- The proof avoids metamathematical techniques.
- Establishes a direct connection between two concepts.

## Abstract

In this paper there is proved without any metamathematical techniques that the existence of precipitous ideals immediately follows from Kuratowski partitions.