One Henkin Quantifier in the Empty Vocabulary Suffices for Undecidability

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. We estimate the size of such quantifiers proving undecidability of $L_{\cancel{0}}({\mathrm{H}}_{12})$ and $L_{\cancel{0}}({\mathrm{E}}_{10})$ .