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Every two elementarily equivalent models have isomorphic ultrapowers


We prove (without G.C.H.) that every two elementarily equivalent models have isomorphic ultrapowers, and some related results.

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The preparation of this paper was supported in Part by NSF Grant GP-22937.

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Shelah, S. Every two elementarily equivalent models have isomorphic ultrapowers. Israel J. Math. 10, 224–233 (1971).

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  • Equivalent Model
  • Regular Cardinal
  • Elementary Classis
  • Alent Model
  • Proper Filter