Completeness is a property of proof systems. Simply put, we want to show that if 0 S p, then there exists a model Msuch that Msatis es but not p. Bruno Bentzen A Formalization of a Henkin-style Completeness Proof … An … Probably best known is the proof of Leon Henkin (1921- ). Proof sketch (Henkin) The proof follows by (reverse) contraposition and it is thus non-constructive. The last part of this study is devoted to Henkin's work concerning the generalization of his completeness proof to any logic from his initial work in type theory. He received his PhD from the Indian Statistical Institute in 1980. In 1963 Henkin published a completeness proof for propositional type theory, A Theory of Propositional Types, where he devised yet another method not directly based on his completeness proof for the whole theory of types. obtained the proof of completeness of –rst order logic readapting the ar-gument found for the theory of types. The Completeness Theorem of Godel 2. Henkin did not use the "weak/strong" terminology at that time, but in 1996 he claimed that in his 1947 doctoral dissertation at Princeton University he had proved strong completeness for the first-order calculus. The proof here is in essence a Henkin-style argument of building models out of constants (which is at the heart of Joyal's completeness theorem), and which avoids the non-constructive detours of the usual first-order version of the proof you sketched. Acknowledgements This research has been possible thanks to the research project sustained by Ministry of Science and Innovation of Spain with reference FFI-2009-09345MICINN. Henkin’s completeness proof can be applied to classical logic as well. His research interests are in descriptive set theory. The Discovery of My Completeness Proofs - Volume 2 Issue 2 - Leon Henkin I Part 1. Weak completeness follows trivially as a corollary to Henkin's proof. Roughly, we say that a proof system is complete iff truth implies derivability. Henkin's completness proof for first order logic (using his method of constants) and Henkin's work on the completeness of type theory were both carried out in his doctoral 1947 dissertation written under the direction of Alonzo Church. Since a classical prime theory must be complete (prove either φ or ¬ φ for all sentences φ ) and admits only conservative extensions, the Kripke model constructed in the proof of Theorem 8.6.7 collapses to one state, and we obtain a classical structure. "Henkin-proofs", do not seem to make any reference to any deductive system at all. Henkin's Proof for First Order Logic S M Srivastava is with the Indian Statistical, Institute, Calcutta. Yet, the proofs for FOL we usually find in logic textbooks, i.e.

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