Abstract
Keisler [1965] contains a modification of the method of constant which results in the construction of Henkin models which are essentially ultraproducts. It was observed in the last chapter that there are fs sets in K which cannot be extended to mfs and term complete sets in K. Given S, afs set of sentences in K, it was shown that new individual constant can be added to K in such a way that S has a mfs and term-complete extension in the larger language. Rather than add just any set of new individual constant, Keisler added the direct product of a family of sets. As a consequence, the resulting Henkil model (when restricted to K) is isomorphic to an ultraproduct.
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References
Keisler, H. J., A Survey of Ultraproducts, Logic, Methodology and Philosophy of Science, Y. Bar-Hillel, editor (North Holland, Amsterdam) 112–126, 1965.
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© 1997 Kluwer Academic Publishers
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(1997). Keisler,s Specialization of the Method of Constants. In: Henkin-Keisler Models. Mathematics and Its Applications, vol 392. Springer, Boston, MA. https://doi.org/10.1007/978-0-585-28844-4_2
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DOI: https://doi.org/10.1007/978-0-585-28844-4_2
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-7923-4366-0
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