Lattices of Intermediate Theories via Ruitenburg's Theorem
Logic
2023-03-21 v1
Abstract
For every univariate formula we introduce a lattices of intermediate theories: the lattice of -logics. The key idea to define chi-logics is to interpret atomic propositions as fixpoints of the formula , which can be characterised syntactically using Ruitenburg's theorem. We develop an algebraic duality between the lattice of -logics and a special class of varieties of Heyting algebras. This approach allows us to build five distinct lattices corresponding to the possible fixpoints of univariate formulas|among which the lattice of negative variants of intermediate logics. We describe these lattices in more detail.
Keywords
Cite
@article{arxiv.2004.00989,
title = {Lattices of Intermediate Theories via Ruitenburg's Theorem},
author = {Gianluca Grilletti and Davide Emilio Quadrellaro},
journal= {arXiv preprint arXiv:2004.00989},
year = {2023}
}