Abstract
Leon Henkin (1921–2006) was not only an extraordinary logician, but also an excellent teacher, a dedicated professor and an exceptional person. The first two sections of this paper are biographical, discussing both his personal and academic life. In the last section we present three aspects of Henkin’s work. First we comment part of his work fruit of his emphasis on teaching. In a personal communication he affirms that On mathematical induction, published in 1969, was the favourite among his articles with a somewhat panoramic nature and not meant exclusively to specialists. This subject is covered in the first subsection. Needless to say that we also analyse Henkin’s better known contribution: his completeness method. His renowned results on completeness for both type theory and first order logic were part of his thesis, The Completeness of Formal Systems, presented at Princeton in 1947 under the advise of Alonzo Church. It is interesting to note that he obtained the proof of completeness for first order logic readapting the argument for the theory of types. The last subsection is devoted to philosophy. The work most directly related to philosophy is an article entitled: Some Notes on Nominalism which appeared in the Journal of Symbolic Logic in 1953. Unfortunately, we are not covering his contribution to the field of cylindric algebras. As a matter of fact, Henkin spent many years investigating algebraic structures with Alfred Tarski and Donald Monk, among others.
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Notes
Written by John Addison, William Craig, Caroline Kane and Alan Schoenfeld.
See PMC14 and PMC19.
See (Henkin (1996), p. 132).
Church (1951) explained what was to become his paper on that subject.
Henkin (1978), class notes.
Henkin (1978), class notes.
We strongly recommend a reading of Henkin’s paper The discovery of my completeness proofs—Henkin (1996)—on which the following exposition relies.
In (Henkin (1996), p. 151).
In (Henkin (1996), p. 141).
In Completeness: from Gödel to Henkin (Manzano and Alonso 2013) readers will find a more elaborated treatment of the historical aspects of completeness.
“This may seem curious, as his work in logic, and his teaching, placed great emphasis to the constructive character of mathematical logic, while the model theory to which I contributed is filled with theorems about very large classes of mathematical structures, whose proofs often by-pass constructive methods”. In (Henkin (1996), p. 127).
See the discussion surrounding the relation between Peano models and induction models in (Henkin (1960), Sect. 5).
(Henkin (1953b), p. 19).
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Manzano, M., Alonso, E. Visions of Henkin. Synthese 192, 2123–2138 (2015). https://doi.org/10.1007/s11229-013-0389-7
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DOI: https://doi.org/10.1007/s11229-013-0389-7