On Reductions of Hintikka Sets for Higher-Order Logic

TL;DR

This paper demonstrates how properties of Hintikka sets in higher-order logic can be reduced to existing properties, leading to a new model existence theorem for these reduced properties.

Contribution

It introduces a reduction of Steen's Hintikka set properties to Brown's, enabling derivation of a model existence theorem in higher-order logic.

Findings

Reduction of Steen's properties to Brown's properties

Derivation of a model existence theorem for Steen's properties

Establishment of a connection between different Hintikka set frameworks

Abstract

Steen's (2018) Hintikka set properties for Church's type theory based on primitive equality are reduced to the Hintikka set properties of Brown (2007). Using this reduction, a model existence theorem for Steen's properties is derived.