# A herbrandized functional interpretation of classical first-order logic

A herbrandized functional interpretation of classical first-order logic 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

# A herbrandized functional interpretation of classical first-order logic

, Volume 56 (6) – May 19, 2017
17 pages

/lp/springer_journal/a-herbrandized-functional-interpretation-of-classical-first-order-qqexnQ43qe
Publisher
Springer Berlin Heidelberg
Subject
Mathematics; Mathematical Logic and Foundations; Mathematics, general; Algebra
ISSN
0933-5846
eISSN
1432-0665
D.O.I.
10.1007/s00153-017-0555-6
Publisher site
See Article on Publisher Site

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