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On the cofinality of ultrapowers

  • Andreas Blass (a1) and Heike Mildenberger (a2)

Abstract

We prove some restrictions on the possible cofinalities of ultrapowers of the natural numbers with respect to ultrafilters on the natural numbers. The restrictions involve three cardinal characteristics of the continuum, the splitting number s, the unsplitting number r, and the groupwise density number g. We also prove some related results for reduced powers with respect to filters other than ultrafilters.

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[1] Blass, A., Near Coherence of filters, I: Cofinal equivalence of models of arithmetic, Notre Dame Journal of Formal Logic, vol. 27 (1986), pp. 579591.
[2] Blass, A., Applications of superperfect forcing and its relatives, Set theory and its applications (Steprāns, J. and Watson, S., editors), Lecture Notes in Mathematics, no. 1401, Springer-Verlag, 1989, pp. 1840.
[3] Blass, A. and Shelah, S., There may be simple - and -points and the Rudin-Keisler ordering may be downward directed, Annals of Pure and Applied Logic, vol. 33 (1987), pp. 213243.
[4] Canjar, R. M., Model-Theoretic Properties of Countable Ultraproducts Without the Continuum Hypothesis, Ph.D. thesis , University of Michigan, 1982.
[5] Canjar, R. M., Countable ultraproducts without CH, Annals of Pure and Applied Logic, vol. 37 (1988), pp. 179.
[6] Canjar, R. M., Cofinalities of countable ultraproducts: the existence theorem, Notre Dame Journal of Formal Logic, vol. 30 (1989), pp. 539542.
[7] Nyikos, P., Special ultrafilters and cofinal subsets ofωω, (to appear).
[8] Roitman, J., Non-isomorphic H-fields from non-isomorphic ultrapowers, Mathematische Zeitschrift, vol. 181 (1982), pp. 9396.
[9] Solomon, R. C., Families of sets and functions, Czechoslovak Mathematical Journal, vol. 27 (1977), pp. 556559.
[10] van Douwen, E., The integers and topology, Handbook of Set Theoretic Topology (Kunen, K. and Vaughan, J., editors), North-Holland, 1984, pp. 111167.
[11] Vaughan, J., Small uncountable cardinals and topology, Open Problems in Topology (van Mill, J. and Reed, G., editors), North-Holland, 1990, pp. 195218.

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On the cofinality of ultrapowers

  • Andreas Blass (a1) and Heike Mildenberger (a2)

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