Can I read First steps towards a formalization of Forcing on EtoBox?

First steps towards a formalization of Forcing by Gunther, Emmanuel; Pagano, Miguel; Terraf, Pedro Sánchez is a scholarly article available to read on EtoBox.

What is First steps towards a formalization of Forcing about?

We lay the ground for an Isabelle/ZF formalization of Cohen's technique of forcing. We formalize the definition of forcing notions as preorders with top, dense subsets, and generic filters. We formalize the definition of forcing notions as preorders with top, dense subsets, and generic filters. We formalize a version of the principle of Dependent Choices and using it we prove the Rasiowa-Sikorski lemma on the existence of generic filters. Given a transitive set $M$, we define its generic extension $M[G]$, the canonical names for elements of $M$, and finally show that if $M$ satisfies the axiom of pairing, then $M[G]$ also does. We also prove $M[G]$ is transitive.

Author

Gunther, Emmanuel; Pagano, Miguel; Terraf, Pedro Sánchez

Published

2018

Language

EN