Truth values algebras and proof normalization
Logic in Computer Science
2023-05-15 v1
Abstract
We extend the notion of Heyting algebra to a notion of truth values algebra and prove that a theory is consistent if and only if it has a B-valued model for some non trivial truth values algebra B. A theory that has a B-valued model for all truth values algebras B is said to be super-consistent. We prove that super-consistency is a model-theoretic sufficient condition for strong normalization.
Keywords
Cite
@article{arxiv.2305.07311,
title = {Truth values algebras and proof normalization},
author = {Gilles Dowek},
journal= {arXiv preprint arXiv:2305.07311},
year = {2023}
}