4 papers · 1 filter
The doctrinal Gödel's completeness theorem and the type space functor
Marco Abbadini, Francesca Guffanti
We give a self-contained proof of Gödel's completeness theorem entirely within the formalism of first-order Boolean doctrines (an algebraic approach to classical many-sorted first…
Freely adding one layer of quantifiers to a Boolean doctrine
Marco Abbadini, Francesca Guffanti
We describe the layer of quantifier alternation depth at most one of the quantifier completion of a Boolean doctrine over a small category. This amounts to a doctrinal version of H…
The unification type of Lukasiewicz logic with a bounded number of variables
Marco Abbadini, Luca Spada
Building on the correspondence between finitely axiomatised theories in Åukasieiwcz logic and rational polyhedra, we prove that the unification type of the fragment of Åukasiewic…
Quantifier-free formulas and quantifier alternation depth in doctrines
Marco Abbadini, Francesca Guffanti
This paper aims to incorporate the notion of quantifier-free formulas modulo a first-order theory and the stratification of formulas by quantifier alternation depth modulo a first-…