Notre Dame Journal of Formal Logic

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

Victor Pambuccian

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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.

Article information

Source
Notre Dame J. Formal Logic, Volume 59, Number 1 (2018), 75-90.

Dates
Received: 22 March 2014
Accepted: 1 June 2015
First available in Project Euclid: 1 September 2017

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1504252824

Digital Object Identifier
doi:10.1215/00294527-2017-0019

Mathematical Reviews number (MathSciNet)
MR3744352

Zentralblatt MATH identifier
06848192

Subjects
Primary: 03F07: Structure of proofs
Secondary: 03B30: Foundations of classical theories (including reverse mathematics) [See also 03F35] 51F05: Absolute planes

Keywords
Steiner–Lehmus theorem direct proof indirect proof sequent calculus absolute geometry

Citation

Pambuccian, Victor. Negation-Free and Contradiction-Free Proof of the Steiner–Lehmus Theorem. Notre Dame J. Formal Logic 59 (2018), no. 1, 75--90. doi:10.1215/00294527-2017-0019. https://projecteuclid.org/euclid.ndjfl/1504252824


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