Horn classes and reduced direct products
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- by Richard Mansfield PDF
- Trans. Amer. Math. Soc. 172 (1972), 279-286 Request permission
Abstract:
Boolean-valued model theory is used to give a direct proof that an $E{C_\Delta }$ model class closed under reduced direct products can be characterized by a set of Horn sentences. Previous proofs by Keisler and Galvin used either the G. C H. or involved axiomatic set theory.References
- Fred Galvin, Horn sentences, Ann. Math. Logic 1 (1970), no. 4, 389–422. MR 325382, DOI 10.1016/0003-4843(70)90002-1
- H. Jerome Keisler, Reduced products and Horn classes, Trans. Amer. Math. Soc. 117 (1965), 307–328. MR 170812, DOI 10.1090/S0002-9947-1965-0170812-4
- Richard Mansfield, The theory of Boolean ultrapowers, Ann. Math. Logic 2 (1970/71), no. 3, 297–323. MR 300887, DOI 10.1016/0003-4843(71)90017-9 D. Scott and R. M. Solovay, Boolean-valued models of set theory, Proc. Sympos. Pure Math., vol. 13, part 2, Amer. Math. Soc., Providence, R. I. (to appear).
- Saharon Shelah, Every two elementarily equivalent models have isomorphic ultrapowers, Israel J. Math. 10 (1971), 224–233. MR 297554, DOI 10.1007/BF02771574
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 172 (1972), 279-286
- MSC: Primary 02H05
- DOI: https://doi.org/10.1090/S0002-9947-1972-0317924-3
- MathSciNet review: 0317924