DeepAI AI Chat
Log In Sign Up

Mechanization of Separation in Generic Extensions

01/10/2019
by   Emmanuel Gunther, et al.
0

We mechanize, in the proof assistant Isabelle, a proof of the axiom-scheme of Separation in generic extensions of models of set theory by using the fundamental theorems of forcing. We also formalize the satisfaction of the axioms of Extensionality, Foundation, Union, and Powerset. The axiom of Infinity is likewise treated, under additional assumptions on the ground model. In order to achieve these goals, we extended Paulson's library on constructibility with renaming of variables for internalized formulas, improved results on definitions by recursion on well-founded relations, and sharpened hypotheses in his development of relativization and absoluteness.

READ FULL TEXT

page 1

page 2

page 3

page 4

10/27/2022

The formal verification of the ctm approach to forcing

We discuss some highlights of our computer-verified proof of the constru...
08/21/2013

Formalization, Mechanization and Automation of Gödel's Proof of God's Existence

Gödel's ontological proof has been analysed for the first-time with an u...
04/28/2023

A Critique of Czerwinski's "Separation of PSPACE and EXP"

Czerwinski's paper "Separation of PSPACE and EXP" [Cze21] claims to prov...
01/27/2020

Formalization of Forcing in Isabelle/ZF

We formalize the theory of forcing in the set theory framework of Isabel...
07/13/2018

First steps towards a formalization of Forcing

We lay the ground for an Isabelle/ZF formalization of Cohen's technique ...
03/27/2013

d-Separation: From Theorems to Algorithms

An efficient algorithm is developed that identifies all independencies i...
11/09/2017

h: A Plank for Higher-order Attribute Contraction Schemes

We present and formalize h, a core (or "plank") calculus that can serve ...