Sealing from Iterability

TL;DR

This paper introduces a new forcing technique to achieve sealing in set theory using a self-iterable model, emphasizing a simplified, fine-structure free approach that enhances accessibility.

Contribution

It presents a novel, fine-structure free method for sealing via forcing over self-iterable models, simplifying the proof process in iteration theory.

Findings

Sealing achieved through forcing over self-iterable models.

Proofs are simplified by avoiding fine-structure complexity.

Approach aims to make iteration theory more accessible.

Abstract

We obtain sealing by forcing over a self-iterable model. The proof is fine-structure free and uses only basic ideas from iteration theory. We believe that such fine-structure free proofs will make the subject more accessible to the general set theoretic community.