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Ramsey Algebras and Ramsey Spaces

Teh, Wen Chean
http://rave.ohiolink.edu/etdc/view?acc_num=osu1357244115

Abstract Details

2013, Doctor of Philosophy, Ohio State University, Mathematics.
Hindman's theorem says that every finite coloring of the natural numbers has a monochromatic set of finite sums. Galvin and Glazer gave a brilliant simple proof of Hindman's theorem using idempotent ultrafilters. We study Ramsey algebras, which are structures that satisfy an analogue of Hindman's theorem. We show the existence of idempotent ultrafilters for Ramsey algebras under Martin's axiom, and the existence of idempotent ultrafilters for Ramsey algebras on a countable field of sets. We conclude by studying a class of Ramsey spaces, which arise from Ramsey algebras.
Timothy Carlson (Advisor)
Chris Miller (Committee Member)
Neil Robertson (Committee Member)
101 p.
Mathematics
Ramsey algebra; Ramsey space; reduction; idempotent ultrafilter; strongly reductible; finitely based; weakly Ramsey; orderly term; orderly composition

Recommended Citations

Citations

  • Teh, W. C. (2013). Ramsey Algebras and Ramsey Spaces [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1357244115

    APA Style (7th edition)

  • Teh, Wen Chean. Ramsey Algebras and Ramsey Spaces. 2013. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1357244115.

    MLA Style (8th edition)

  • Teh, Wen Chean. "Ramsey Algebras and Ramsey Spaces." Doctoral dissertation, Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1357244115

    Chicago Manual of Style (17th edition)

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This open access ETD is published by The Ohio State University and OhioLINK.