DeepAI

# Ruitenburg's Theorem via Duality and Bounded Bisimulations

For a given intuitionistic propositional formula A and a propositional variable x occurring in it, define the infinite sequence of formulae A _i | i>1 by letting A_1 be A and A_i+1 be A(A_i/x). Ruitenburg's Theorem [8] says that the sequence A _i (modulo logical equivalence) is ultimately periodic with period 2, i.e. there is N > 0 such that A N+2 A N is provable in intuitionistic propositional calculus. We give a semantic proof of this theorem, using duality techniques and bounded bisimulations ranks.

• 12 publications
• 15 publications
01/04/2019

### Free Heyting Algebra Endomorphisms: Ruitenburg's Theorem and Beyond

Ruitenburg's Theorem says that every endomorphism f of a finitely genera...
04/18/2018

### Duality between unprovability and provability in forward proof-search for Intuitionistic Propositional Logic

The inverse method is a saturation based theorem proving technique; it r...
04/30/2019

### Case Study of the Proof of Cook's theorem - Interpretation of A(w)

Cook's theorem is commonly expressed such as any polynomial time-verifia...
12/28/2021

### A General Glivenko-Gödel Theorem for Nuclei

Glivenko's theorem says that, in propositional logic, classical provabil...
04/06/2020

### A limitation on the KPT interpolation

We prove a limitation on a variant of the KPT theorem proposed for propo...
10/31/2021

### Size Matters in Univalent Foundations

We investigate predicative aspects of constructive univalent foundations...
12/09/2022

### The unstable formula theorem revisited

We first prove that Littlestone classes, those which model theorists cal...