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R. Statman (1979)
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Q. Puite (2000)
MATHEMATICAL LOGIC
Fernando Ferreira, Ana Nunes (2006)
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herbrandized
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ii ) For each type σ there are denumerably many variables of type σ : x σ , y σ , z σ , etc. Variables
b) ( ¬ φ ) p is ¬ ( φ p ), ( φ ∧ ψ ) p is φ p ∧ ψ p , and ( φ ∨ ψ ) p is φ p ∨ ψ
J. Avigad, H. Towsner (2008)
Functional interpretation and inductive definitionsThe Journal of Symbolic Logic, 74
P. Gerhardy, U. Kohlenbach (2003)
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V. Gödel (1958)
ÜBER EINE BISHER NOCH NICHT BENÜTZTE ERWEITERUNG DES FINITEN STANDPUNKTESDialectica, 12
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Justus Diller (2002)
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c) Let q be a closed term of type τ ∗ and r be a closed term of type τ → σ ∗ . Suppose that u is a closed term of type τ , and assume that u ∈ q s and t ∈ ( ru ) s . Then t ∈ ( (cid:83) qr ) s
A. Troelstra, H. Schwichtenberg (1996)
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Fernando Ferreira, Paulo Oliva (2005)
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B. Berg, E. Briseid, P. Safarik (2011)
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Let t be a term of star type
J Avigad, S Feferman (1998)
Handbook of Proof Theory, Studies in Logic and the Foundations of Mathematics
We introduce a new typed combinatory calculus with a type constructor that, to each type $$\sigma $$ σ , associates the star type $$\sigma ^*$$ σ ∗ of the nonempty finite subsets of elements of type $$\sigma $$ σ . We prove that this calculus enjoys the properties of strong normalization and confluence. With the aid of this star combinatory calculus, we define a functional interpretation of first-order predicate logic and prove a corresponding soundness theorem. It is seen that each theorem of classical first-order logic is connected with certain formulas which are tautological in character. As a corollary, we reprove Herbrand’s theorem on the extraction of terms from classically provable existential statements.
Archive for Mathematical Logic – Springer Journals
Published: May 19, 2017
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