Leon Henkin

Leon Albert Henkin (April 19, 1921, Brooklyn, New York – November 1, 2006, Oakland, California) was an American logician, whose works played a strong role in the development of logic, particularly in the theory of types.

He was an active scholar at the University of California, Berkeley, where he made great contributions as a researcher and teacher, as well as in administrative positions.

[6] Leon Albert Henkin was born on April 19, 1921, in Brooklyn, New York, to a Jewish family that had emigrated from Russia a generation earlier.

[2] In the years of his high school education, Henkin considered becoming a math teacher and also came to desire to become a writer (as he later expressed in a personal letter).

[10] This reading was highly significant for Henkin, not so much because of the content itself, but because with it he discovered that he could understand the research on logic and mathematics that was taking place at the time.

[7] According to Henkin, although he managed to follow Quine's demonstration, he did not manage to capture the idea of the proof: "I simply noted that the aim of the paper was to show that every tautology had a formal proof in the system of axioms presented, and I expended my utmost effort to check Quine's reasoning that this was so, without ever reflecting on why author and reader were making this effort.

Days before the war broke out, the Polish mathematician and logician Alfred Tarski had come to Harvard, at Quine's invitation, to give a series of lectures on logic.

In it Tarski spoke of Gödel's work on undecidable propositions in Type Theory and on the existence of decision algorithms for formal systems, a subject that Henkin found extremely stimulating.

[7] In his last year at Columbia, in 1941, Professor F. J. Murray, knowing that Henkin was a mathematics student interested in Logic, suggested that they review together the monograph by Gödel recently published at Princeton on the consistency of the axiom of choice with the generalized continuum hypothesis.

Although the meetings they had to discuss it were scarce and Leon ended up revising this monograph practically alone, the experience was considered by him as the most enriching one in his formation at Columbia.

He had to rush his oral qualification exam, with which he obtained the degree of M. A. and left Princeton to take part in the Manhattan Project.

This interruption would last four years, during which he contributed his mathematical knowledge working on radar problems and in the design of a plant to separate uranium isotopes.

Upon his return, he joined the logic course that Church had begun a month earlier on Frege's theory of "sense and reference".

[7] These results, as well as others that other that emerged from the same ideas, came to take part in Henkin's doctoral dissertation, which was titled "The completeness of formal systems", with which he graduated in June 1947.

During this time, in 1948, he met Ginette Potvin, during a trip to Montreal with his sister Estelle and Princeton mathematics graduate student Harold Kuhn.

However, Henkin did not want to accept it, as he was sympathetic to the protests recently raised by the controversial oath of allegiance that had been required of university professors since 1950.

It was he who brought me to Berkeley in 1953, so I owe much to him personally as well as scientifically.”[17] Tarski not only offered Henkin a job opportunity but also provided him with a very fertile interdisciplinary collaborative environment for the development of Logic.

In addition to the dedication he put in his teaching as well as in guiding the Group in Logic and the Methodology of Science, he held some administrative positions; he was director of the Department of Mathematics from 1966 to 1968, and subsequently from 1983 to 1985.

[2] Always kind to his students and colleagues, whom he frequently invited to his home to enjoy evenings with Ginette, he is remembered as a brilliant researcher, a teacher committed to his discipline and a person who showed solidarity with his community.

Both presented part of the results exposed in the dissertation "The completeness of formal systems" with which Henkin received his Ph.D. degree at Princeton in 1947.

Other results central to model theory are obtained as corollaries of the strong completeness of the first-order logic proved by Henkin.

[36] However, Henkin simplifies the difficult task of tracing the development and shaping of his ideas by his article "The discovery of my completeness proofs",[7] published in 1996.

As soon as he arrived at Princeton, he attended Church's course in logic that had begun one month earlier, which dealt with Frege's theory of "sense and reference".

To make each expression correspond to the element it denotated, he needed a choice function, in whose search Henkin invested many efforts.

The discussions relevant to this philosophical doctrine arise naturally in the proofs of completeness given by Henkin, as well as in his proposal for a change in semantics through general models.

[49] In the words of one of his students, "part of his magic was his elegant expression of the mathematics, but he also worked hard to engage his audience in conjecturing and seeing the next step or in being surprised by it.

He considered it important that the students could follow the rhythm of the class, even if this meant that some would find it slow –they could continue at their own pace with the readings.

These changes form themselves into rivulets and streams that merge at various angles with those arising in parts of our society quite different from education, mathematics, or science.

[2] Diane Resek, one of his students with an affinity for teaching, described him as follows: "Leon was committed to work toward equity in society.

"[62]Aware of the contributions that mathematicians could make through teaching, Henkin defended that teaching should be valued in the academy environment, as he expressed in a personal letter: "In these times when our traditionally trained mathematics Ph.D.’s are finding rough going in the marketplace, it seems to me that we on the faculty should particularly seek new realms wherein mathematics training can make a substantial contribution to the basic aims of society.