Archive for Mathematical Logic

, Volume 43, Issue 3, pp 297–309 | Cite as

Proof-theoretical analysis of order relations

  • Sara NegriEmail author
  • Jan von Plato
  • Thierry Coquand


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.


Partial Order Linear Order Order Relation Elementary Theory Sequent Calculus 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of PhilosophyFinland
  2. 2.Department of Computer ScienceChalmess University of TechnologyGöteborgSweden

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