Ultrafilter mappings and their Dedekind cuts
نویسندگان
چکیده
منابع مشابه
forR1 ultrafilter mappings and their Dedekind cuts
Associated to each ultrafilter U on ω and each map p : ω → ω is a Dedekind cut in the ultrapower ω/p(U). Blass has characterized, under CH, the cuts obtainable when U is taken to be either a p-point ultrafilter, a weakly-Ramsey ultrafilter or a Ramsey ultrafilter. Dobrinen and Todorcevic have introduced the topological Ramsey spaceR1. Associated to the spaceR1 is a notion of Ramsey ultrafilter ...
متن کاملUltrafilter Mappings and Their Dedekind Cuts
Let D be an ultrafilter on the set N of natural numbers. To each function p: N — N and each ultrafilter E that is mapped to D by p, we associate a Dedekind cut in the ultrapower ö-prod N. We characterize, in terms of rather simple closure conditions, the cuts obtainable in this manner when various restrictions are imposed on E and p. These results imply existence theorems, some known and some n...
متن کاملRamsey for R1 ultrafilter mappings and their Dedekind cuts
Associated to each ultrafilter U on ω and each map p : ω → ω is a Dedekind cut in the ultrapower ωω/p(U). Blass has characterized, under CH, the cuts obtainable when U is taken to be either a p-point ultrafilter, a weakly-Ramsey ultrafilter or a Ramsey ultrafilter. Dobrinen and Todorcevic have introduced the topological Ramsey space R1. Associated to the space R1 is a notion of Ramsey ultrafilt...
متن کاملSupplementary Notes on Dedekind Cuts
Motivation: Our textbook discusses and even proves many properties of R, the field of real numbers; but it doesn’t define it. I felt that it would be rather awkward to discuss real numbers without knowing what they were and I decided to write some notes on the construction of R. The approach I am following is called ‘Dedekind cut’, discovered by a German mathematician, Richard Dedekind (1831-19...
متن کاملThe Elementary Theory of Dedekind Cuts
Contents 1. Introduction. 2. Heirs. 3. The invariance group of a cut. 4. Review of T-convex valuation rings. 5. The invariance valuation ring of a cut. 6. A method for producing cuts with given signature. 7. Existentially closed extensions. 8. The elementary theory of convex subgroups. 9. The elementary theory of cuts. 10. Counter examples. 1. Introduction. Let X be a totally ordered set. A (De...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1974
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1974-0351822-6