Abstract
This is a personal reminiscence about the work I did under the direction of Leon Henkin during the last year of my graduate studies, work that proved to be fortuitous in the absence of Alfred Tarski, my thesis advisor.
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Notes
- 1.
Throughout, I use “interpretable” here to mean relatively interpretable in the sense of Tarski, Mostowski, and Robinson; see [20].
- 2.
Actually, a further simplification of Henkin’s argument due to Hasenjaeger (see [10]) became the preferred mode of presentation.
- 3.
I was pleased to learn in 1957 that Andrzej Ehrenfeucht obtained the sought-for decidability results; he applied back-and-forth methods rather than the elimination of quantifier methods that Tarski had expected. And, as it later turned out, the basic idea of generalized powers that I had introduced to reduce the decision problem could be combined in a fruitful way with the work of my fellow student Bob Vaught on sentences preserved under Cartesian products, leading to the paper Feferman and Vaught [7] on generalized products of theories.
- 4.
Years later, I learned from Steve Givant that this was the standard route for proving the representation theorem, but I have not checked the literature to see exactly how it is usually presented.
- 5.
Tarski told John Corcoran that he considered himself to be “the greatest living sane logician”; cf. [1, p. 5]. My frustrations working with Tarski as a student were by no means unique as is testified to in the many stories in that biography.
- 6.
- 7.
As is well known nowadays, this can be improved to arbitrary recursively enumerable extensions of the fragment Σ 1-IA of PA and even weaker theories.
- 8.
See Visser [24] for a full exploration of the phenomenon of interpretability of inconsistency.
- 9.
I spent the first year at Stanford writing up my thesis (see [2]) and received the Ph.D. at UC Berkeley in 1957.
- 10.
- 11.
Orey had heard me talk about my thesis work at the Institute for Symbolic Logic held at Cornell in the summer of 1957, and that led him to his theorem, which he kindly let me include in my 1960 publication; cf. also Orey [19].
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Acknowledgements
I wish to thank Anita Burdman Feferman and Albert Visser for their helpful comments on a draft of this article.
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Feferman, S. (2014). A Fortuitous Year with Leon Henkin. In: Manzano, M., Sain, I., Alonso, E. (eds) The Life and Work of Leon Henkin. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-09719-0_5
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