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Transactions of the American Mathematical Society

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Horn classes and reduced direct products

Author: Richard Mansfield
Journal: Trans. Amer. Math. Soc. 172 (1972), 279-286
MSC: Primary 02H05
MathSciNet review: 0317924
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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 [Enhancements On Off] (What's this?)

  • [1] F. Galvin, Horn sentences, Ann. Math. Logic 1 (1970), 389-422. MR 0325382 (48:3729)
  • [2] H. J. Keisler, Reduced products and Horn classes, Trans. Amer. Math. Soc. 117 (1965), 307-328. MR 30 #1047. MR 0170812 (30:1047)
  • [3] R. Mansfield, The theory of Boolean ultrapowers, Ann. Math. Logic 2 (1971), 297-323. MR 0300887 (46:47)
  • [4] 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).
  • [5] S. Shelah, Every two elementarily equivalent models have isomorphic ultrapowers, Israel J. Math. 10 (1971), 224-234. MR 0297554 (45:6608)

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