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Negation-Free and Contradiction-Free Proof of the Steiner–Lehmus Theorem
Notre Dame Journal of Formal Logic 59 (1):75-90 (2018)
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.Other Versions
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References found in this work
Cut Elimination in the Presence of Axioms.Sara Negri & Jan Von Plato - 1998 - Bulletin of Symbolic Logic 4 (4):418-435.
Contraction-free sequent calculi for geometric theories with an application to Barr's theorem.Sara Negri - 2003 - Archive for Mathematical Logic 42 (4):389-401.
Propositions in Prepositional Logic Provable Only by Indirect Proofs.Jan Ekman - 1998 - Mathematical Logic Quarterly 44 (1):69-91.
A common axiom set for classical and intuitionistic plane geometry.Melinda Lombard & Richard Vesley - 1998 - Annals of Pure and Applied Logic 95 (1-3):229-255.
An Intuitionistic Axiomatisation of Real Closed Fields.Erik Palmgren - 2002 - Mathematical Logic Quarterly 48 (2):297-299.
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