# Changing measurable into small accessible cardinals

## TL;DR

This paper provides a detailed proof of the properties of Prikry type forcing, demonstrating how it transforms a measurable cardinal into leph_omega, with implications for set theory and large cardinal axioms.

## Contribution

It offers a comprehensive proof of Prikry forcing properties specifically for turning a measurable cardinal into leph_omega, clarifying its set-theoretic effects.

## Key findings

- Confirmed the properties of Prikry forcing in this context
- Established the transformation of measurable cardinals to leph_omega
- Enhanced understanding of forcing techniques for large cardinals

## Abstract

We give a detailed proof of the properties of the usual Prikry type forcing notion for turning a measurable cardinal into $\aleph_\omega$.