End extensions, conservative extensions, and the Rudin-Frolík ordering
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- by Andreas Blass PDF
- Trans. Amer. Math. Soc. 225 (1977), 325-340 Request permission
Abstract:
The ordering of ultrafilters on the natural numbers defined by “E-prod N is an end extension of D-prod N,” the ordering defined by “E-prod N is a conservative extension of D-prod N,” and the Rudin-Frolik ordering are proved to be distinct if the continuum hypothesis holds. These three orderings are also characterized in terms of (not necessarily internal) ultrafilters in the Boolean algebra of internal sets of natural numbers in a nonstandard universe.References
-
A. Blass, Orderings of ultrafilters, Thesis, Harvard Univ., 1970.
- Andreas Blass, On certain types and models for arithmetic, J. Symbolic Logic 39 (1974), 151–162. MR 369050, DOI 10.2307/2272355 —, Amalgamation of non-standard models of arithmetic, J. Symbolic Logic (to appear).
- David Booth, Ultrafilters on a countable set, Ann. Math. Logic 2 (1970/71), no. 1, 1–24. MR 277371, DOI 10.1016/0003-4843(70)90005-7
- Zdeněk Frolík, Sums of ultrafilters, Bull. Amer. Math. Soc. 73 (1967), 87–91. MR 203676, DOI 10.1090/S0002-9904-1967-11653-7
- H. Jerome Keisler, Ultraproducts and saturated models, Nederl. Akad. Wetensch. Proc. Ser. A 67 = Indag. Math. 26 (1964), 178–186. MR 0168483, DOI 10.1016/S1385-7258(64)50021-9
- Kenneth Kunen, Ultrafilters and independent sets, Trans. Amer. Math. Soc. 172 (1972), 299–306. MR 314619, DOI 10.1090/S0002-9947-1972-0314619-7
- K. Kuratowski, Topology. Vol. I, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1966. New edition, revised and augmented; Translated from the French by J. Jaworowski. MR 0217751 D. Lascar, Ultrafiltres et theories stables (to appear).
- R. G. Phillips, Omitting types in arithmetic and conservative extensions, Victoria Symposium on Nonstandard Analysis (Univ. Victoria, Victoria, B.C., 1972) Lecture Notes in Math., Vol. 369, Springer, Berlin, 1974, pp. 195–202. MR 0476499
- Robert G. Phillips, A minimal extension that is not conservative, Michigan Math. J. 21 (1974), 27–32. MR 347591
- Mary Ellen Rudin, Partial orders on the types in $\beta N$, Trans. Amer. Math. Soc. 155 (1971), 353–362. MR 273581, DOI 10.1090/S0002-9947-1971-0273581-5
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 225 (1977), 325-340
- MSC: Primary 02H13; Secondary 04A05
- DOI: https://doi.org/10.1090/S0002-9947-1977-0424556-X
- MathSciNet review: 0424556