Search ETDs:
Ramsey Algebras and Ramsey Spaces
Teh, Wen Chean

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.

Recommended Citations

Hide/Show APA Citation

Teh, W. (2013). Ramsey Algebras and Ramsey Spaces. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

Hide/Show MLA Citation

Teh, Wen Chean. "Ramsey Algebras and Ramsey Spaces." Electronic Thesis or Dissertation. Ohio State University, 2013. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

Hide/Show Chicago Citation

Teh, Wen Chean "Ramsey Algebras and Ramsey Spaces." Electronic Thesis or Dissertation. Ohio State University, 2013. https://etd.ohiolink.edu/

Files

osu1357244115.pdf (639 KB) View|Download