An Explicit Infinite Model Refuting Ulrich's u4 as a Single Axiom for Positive Implication

We construct an explicit infinite model showing that Ulrich's remaining 15-symbol candidate u4 is not a single axiom for positive implicational logic under substitution and modus ponens. The model satisfies every substitution instance of u4 and is closed under modus ponens, while falsifying reflexivity. Subject to the reduction of Fitelson and Peltier (2026), this implies that the minimum single-axiom length is 17 symbols. This deposit is a mathematical resolution submitted for external specialist verification and has not yet undergone peer review.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-18
DOI
https://doi.org/10.5281/zenodo.21987528
Primary Topic
Logic, programming, and type systems
Type
preprint
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preprint

An Explicit Infinite Model Refuting Ulrich's u4 as a Single Axiom for Positive Implication

Byungwoong Yoo
Zenodo (CERN European Organization for Nuclear Research)
Logic, programming, and type systems
preprint

An Explicit Infinite Model Refuting Ulrich's u4 as a Single Axiom for Positive Implication

Byungwoong Yoo
preprint en

Abstract

We construct an explicit infinite model showing that Ulrich's remaining 15-symbol candidate u4 is not a single axiom for positive implicational logic under substitution and modus ponens. The model satisfies every substitution instance of u4 and is closed under modus ponens, while falsifying reflexivity. Subject to the reduction of Fitelson and Peltier (2026), this implies that the minimum single-axiom length is 17 symbols. This deposit is a mathematical resolution submitted for external specialist verification and has not yet undergone peer review.

Zenodo (CERN European Organization for Nuclear Research)
Logic, programming, and type systems
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