This is an announcement for the paper "Ramsey and Nash-Williams combinatorics via Schreier families" by Vassiliki Farmaki.
Abstract: The main results of this paper (a) extend the finite Ramsey partition theorem, and (b) employ this extension to obtain a stronger form of the infinite Nash-Williams partition theorem, and also a new proof of Ellentuck's, and hence Galvin-Prikry's partition theorem. The proper tool for this unification of the classical partition theorems at a more general and stronger level is the system of Schreier families $({\cal A}_{\xi})$ of finite subsets of the set of natural numbers, defined for every countable ordinal $\xi$.
Archive classification: Functional Analysis
Mathematics Subject Classification: Primary 05D10; Secondary 05C55
Remarks: 28 pages, preliminary version
The source file(s), Ramseytheorem.tex: 91989 bytes, is(are) stored in gzipped form as 0404014.gz with size 22kb. The corresponding postcript file has gzipped size 83kb.
Submitted from: combs@mail.ma.utexas.edu
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