The small index property of the Fra\"iss\'e limit of finite Heyting algebras

TL;DR

This paper proves that for the Fra"iss"e limit of finite Heyting algebras, any subgroup of automorphisms with a countable index is closely related to stabilizers of finite sets, revealing a small index property.

Contribution

It establishes the small index property for the automorphism group of the Fra"iss"e limit of finite Heyting algebras, a new result in this area.

Findings

Subgroups with countable index are between pointwise and setwise stabilizers of finite sets.

The automorphism group exhibits the small index property.

Provides insights into the structure of automorphism groups of Heyting algebra limits.

Abstract

We show that if a subgroup of the automorphism group of the Fraisse limit of finite Heyting algebras has a countable index, then it lies between the pointwise and setwise stabilizer of some finite set.