The Rudin-Keisler ordering of $P$-points
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- by Andreas Blass PDF
- Trans. Amer. Math. Soc. 179 (1973), 145-166 Request permission
Abstract:
The Stone-Čech compactification $\beta \omega$ of the discrete space $\omega$ of natural numbers is weakly ordered by the relation “D is the image of E under the canonical extension $\beta f:\beta \omega \to \beta \omega$ of some map $f:\omega \to \omega$.” We shall investigate the structure, with respect to this ordering, of the set of P-points of $\beta \omega - \omega$.References
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A. Blass, Orderings of ultrafilters, Thesis, Harvard University, Cambridge, Mass., 1970.
- Andreas Blass, The intersection of nonstandard models of arithmetic, J. Symbolic Logic 37 (1972), 103–106. MR 323560, DOI 10.2307/2272552
- 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
- Gustave Choquet, Construction d’ultrafiltres sur N, Bull. Sci. Math. (2) 92 (1968), 41–48 (French). MR 234405
- Gustave Choquet, Deux classes remarquables d’ultrafiltres sur N, Bull. Sci. Math. (2) 92 (1968), 143–153 (French). MR 236860
- D. A. Martin and R. M. Solovay, Internal Cohen extensions, Ann. Math. Logic 2 (1970), no. 2, 143–178. MR 270904, DOI 10.1016/0003-4843(70)90009-4
- Richard A. Platek, Eliminating the continuum hypothesis, J. Symbolic Logic 34 (1969), 219–225. MR 256872, DOI 10.2307/2271098
- 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
- Walter Rudin, Homogeneity problems in the theory of Čech compactifications, Duke Math. J. 23 (1956), 409–419. MR 80902
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 179 (1973), 145-166
- MSC: Primary 02H20; Secondary 04A20
- DOI: https://doi.org/10.1090/S0002-9947-1973-0354350-6
- MathSciNet review: 0354350