One Henkin Quantifier in the empty vocabulary suffices for undecidability

TL;DR

The paper demonstrates that adding a specific Henkin quantifier to first-order logic without any additional vocabulary makes the logic undecidable, providing explicit examples of such quantifiers.

Contribution

It introduces the existence of single Henkin quantifiers that cause undecidability in the empty vocabulary, a novel result in logic theory.

Findings

Existence of single Henkin quantifiers leading to undecidability

Explicit examples of such quantifiers provided

Undecidability established in the context of empty vocabulary

Abstract

We prove that there are single Henkin quantifiers such that first order logic augmented by one of these quantifiers is undecidable in the empty vocabulary. Examples of such quantifiers are given.