David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Studia Logica 52 (1):113 - 142 (1993)
This essay demonstrates proof-theoretically the consistency of a type-free theoryC with an unrestricted principle of comprehension and based on a predicate logic in which contraction (A (A B)) (A B), although it cannot holds in general, is provable for a wide range ofA's.C is presented as an axiomatic theoryCH (with a natural-deduction equivalentCS) as a finitary system, without formulas of infinite length. ThenCH is proved simply consistent by passing to a Gentzen-style natural-deduction systemCG that allows countably infinite conjunctions and in which all theorems ofCH are provable.CG is seen to be a consistent by a normalization argument. It also shown that in a senseC is highly non-extensional.
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References found in this work BETA
Dag Prawitz (1965/2006). Natural Deduction: A Proof-Theoretical Study. Dover Publications.
Patrick Suppes (1957/1999). Introduction to Logic. Dover Publications.
Bruce White (1974). A Note on Natural Deduction in Many-Valued Logic. Notre Dame Journal of Formal Logic 15 (1):167-168.
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