The superamalgamation property for reducts of Heyting polyadic algebras with and without equality

TL;DR

This paper investigates the amalgamation properties of reducts of Heyting polyadic algebras of infinite dimension, demonstrating superamalgamation without equality and weaker properties with equality, impacting the understanding of related infinitary intuitionistic logics.

Contribution

It establishes the superamalgamation property for certain reducts of Heyting polyadic algebras and analyzes the effects of equality on these properties.

Findings

Superamalgamation holds for equality-free reducts.

Weaker interpolation properties are found when equality is included.

Results influence the understanding of infinitary intuitionistic logic with equality.

Abstract

We show that several reducts of Heyting polyadic algebras of infinite dimension, with and without equality enjoy various amalgamation properties. In the equality free case we obtain superamalgamation, but when we have equality we obtain a weaker interpolation property, for the corresponding infinitary intuitionistic logic with equality.