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Proof-theoretical analysis of order relations
Archive for Mathematical Logic 43 (3):297-309 (2004)
Abstract
A proof-theoretical analysis of elementary theories of order relations is effected through the formulation of order axioms as mathematical rules added to contraction-free sequent calculus. Among the results obtained are proof-theoretical formulations of conservativity theorems corresponding to Szpilrajn’s theorem on the extension of a partial order into a linear one. Decidability of the theories of partial and linear order for quantifier-free sequents is shown by giving terminating methods of proof-search.Author Profiles
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Citations of this work
Proof analysis in intermediate logics.Roy Dyckhoff & Sara Negri - 2012 - Archive for Mathematical Logic 51 (1):71-92.
Decision methods for linearly ordered Heyting algebras.Sara Negri & Roy Dyckhoff - 2006 - Archive for Mathematical Logic 45 (4):411-422.
Sequent Calculi for $${\mathsf {SCI}}$$ SCI.Szymon Chlebowski - 2018 - Studia Logica 106 (3):541-563.
The Jacobson Radical of a Propositional Theory.Giulio Fellin, Peter Schuster & Daniel Wessel - 2022 - Bulletin of Symbolic Logic 28 (2):163-181.
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