Proof-theoretical analysis of order relations
- 58 Downloads
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.
KeywordsPartial Order Linear Order Order Relation Elementary Theory Sequent Calculus
Unable to display preview. Download preview PDF.
- 2.Cederquist, J., Coquand, Th., Negri, S.: The Hahn-Banach theorem in in type theory. In: G. Sambin and J. Smith, eds, Twenty-Five Years of Constructive Type Theory, Oxford University Press, 1998, pp. 39–50Google Scholar
- 3.Ehrenfeucht, A.: Decidability of the theory of linear order. Notices of the Am. Math. Soc. 6, 268–269 (1959)Google Scholar
- 5.Kreisel, G.: Review of Janiczak (1953). Math. Rev. 15, 669–670 (1954)Google Scholar
- 6.Läuchli, H., Leonard, J.: On the elementary theory of linear order. Fundamenta Mathematicae 59, 109–116 (1966)Google Scholar
- 9.Negri, S., von Plato, J.: Structural Proof Theory. Cambridge University Press, 2001Google Scholar
- 10.Rabin, M.: Decidable theories: In J. Barwise, (ed.), Handbook of Mathematical Logic, North-Holland, Amsterdam, 1977, pp. 595–628Google Scholar
- 11.Scott, D.: Completeness and axiomatizability in many-valued logic. In: Proceedings of the Tarski Symposium, American Mathematical Society, Providence, Rhode Island, 1974, pp. 411–435Google Scholar