DeepAI AI Chat
Log In Sign Up

First steps towards a formalization of Forcing

by   Emmanuel Gunther, et al.

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 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.


page 1

page 2

page 3

page 4


Formalization of Forcing in Isabelle/ZF

We formalize the theory of forcing in the set theory framework of Isabel...

The Generic SysML/KAOS Domain Metamodel

This paper is related to the generalised/generic version of the SysML/KA...

Order polarities

We define an order polarity to be a polarity (X,Y,R) where X and Y are p...

Mechanization of Separation in Generic Extensions

We mechanize, in the proof assistant Isabelle, a proof of the axiom-sche...

Deterministic Conditions for Subspace Identifiability from Incomplete Sampling

Consider a generic r-dimensional subspace of R^d, r<d, and suppose that ...

Generic bivariate multi-point evaluation, interpolation and modular composition with precomputation

Suppose 𝕂 is a large enough field and 𝒫⊂𝕂^2 is a fixed, generic set of p...