Negation-Free and Contradiction-Free Proof of the Steiner–Lehmus Theorem

Victor Pambuccian

doi:10.1215/00294527-2017-0019

Negation-Free and Contradiction-Free Proof of the Steiner–Lehmus Theorem

Victor Pambuccian

Research output: Contribution to journal › Article

2 Scopus citations

Abstract

By rephrasing quantifier-free axioms as rules of derivation in sequent calculus, we show that the generalized Steiner–Lehmus theorem admits a direct proof in classical logic. This provides a partial answer to a question raised by Sylvester in 1852. We also present some comments on possible intuitionistic approaches.

Original language	English (US)
Pages (from-to)	75-90
Number of pages	16
Journal	Notre Dame Journal of Formal Logic
Volume	59
Issue number	1
DOIs	https://doi.org/10.1215/00294527-2017-0019
State	Published - Jan 1 2018

Keywords

Absolute geometry
Direct proof
Indirect proof
Sequent calculus
Steiner–Lehmus theorem

ASJC Scopus subject areas

Logic

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10.1215/00294527-2017-0019

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Pambuccian, V. (2018). Negation-Free and Contradiction-Free Proof of the Steiner–Lehmus Theorem. Notre Dame Journal of Formal Logic, 59(1), 75-90. https://doi.org/10.1215/00294527-2017-0019

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