Contraction-free sequent calculi for geometric theories with an application to Barr's theorem |
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Authors: | Sara Negri |
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Institution: | (1) Department of Philosophy, PL 9, Siltavuorenpenger 20 B, 00014 University of Helsinki, Finland, e-mail: negri@helsinki.fi, FI |
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Abstract: | Geometric theories are presented as contraction- and cut-free systems of sequent calculi with mathematical rules following
a prescribed rule-scheme that extends the scheme given in Negri and von Plato (1998). Examples include cut-free calculi for
Robinson arithmetic and real closed fields. As an immediate consequence of cut elimination, it is shown that if a geometric
implication is classically derivable from a geometric theory then it is intuitionistically derivable.
Received: 18 April 2001 /
Published online: 10 October 2002
Mathematics Subject Classification (2000): 03F05, 18C10, 18B15
Key words or phrases: Cut elimination – Geometric theories – Barr's theorem |
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