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

Corrected and strengthened v2. This release supplies a complete preprint and a Lean 4.33.0 formalization of an explicit substitution-closed infinite countermodel showing that Ulrich's u4 is not a single axiom for positive implicational logic under uniform substitution and modus ponens. Project-run checks include direct Lean compilation, leanchecker, nanoda, a compiled axiom-dependency audit, and a separate Python symbolic checker. Independent third-party specialist review and journal peer review have not yet occurred.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-21
DOI
https://doi.org/10.5281/zenodo.22031656
Primary Topic
Logic, Reasoning, and Knowledge
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, Reasoning, and Knowledge
preprint

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

Byungwoong Yoo
preprint en

Abstract

Corrected and strengthened v2. This release supplies a complete preprint and a Lean 4.33.0 formalization of an explicit substitution-closed infinite countermodel showing that Ulrich's u4 is not a single axiom for positive implicational logic under uniform substitution and modus ponens. Project-run checks include direct Lean compilation, leanchecker, nanoda, a compiled axiom-dependency audit, and a separate Python symbolic checker. Independent third-party specialist review and journal peer review have not yet occurred.

Zenodo (CERN European Organization for Nuclear Research)
Logic, Reasoning, and Knowledge
DOIOpen Access PDFOpenAlex
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An Explicit Infinite Model Refuting Ulrich's u4 as a Single Axiom for Positive Implication — Byungwoong Yoo · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS