Ramsey Algebras and Ramsey Spaces

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.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor dc:publisher

The Ohio State University

Year dc:date

2013

Author dc:creator

• Teh, Wen Chean

Contributors dc:contributor

• Carlson, Timothy

• Mathematics
• Ramsey algebra
• Ramsey space
• reduction
• idempotent ultrafilter
• strongly reductible
• finitely based
• weakly Ramsey
• orderly term
• orderly composition

Statement dc:rights

• unrestricted
• This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.

Language dc:language

English

Repository record dc:identifier

http://rave.ohiolink.edu/etdc/view?acc_num=osu1357244115

OAI identifier oai:identifier

oai:etd.ohiolink.edu:osu1357244115