{"id":{"repo_id":"ohiolink","oai_identifier":"oai:etd.ohiolink.edu:osu1357244115"},"canonical_url":"https://search.dev.ndltd.org/etd/ohiolink/oai:etd.ohiolink.edu:osu1357244115","repository":{"repo_id":"ohiolink","name":"OhioLINK","base_url":"https://etd.ohiolink.edu/acprod/odb_etd/ws/oai/oai"},"display":{"title":"Ramsey Algebras and Ramsey Spaces","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Teh, Wen Chean"],"institution":"The Ohio State University","degree_name":"Doctor of Philosophy","degree_level":"doctoral","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Carlson, Timothy"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-05-21","date_published":"2013-05-21","updated_at":"2026-07-24T03:36:08Z","subjects":["Mathematics","Ramsey algebra","Ramsey space","reduction","idempotent ultrafilter","strongly reductible","finitely based","weakly Ramsey","orderly term","orderly composition"],"languages":["English"],"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."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://rave.ohiolink.edu/etdc/view?acc_num=osu1357244115","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Carlson, Timothy"]},{"key":"dc:creator","label":"Author","values":["Teh, Wen Chean"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2013-05-21"]},{"key":"dc:publisher","label":"Institution","values":["The Ohio State University / OhioLINK"]},{"key":"dc:type","label":"Dc Type","values":["Electronic Thesis or Dissertation"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["The Ohio State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","Ramsey algebra","Ramsey space","reduction","idempotent ultrafilter","strongly reductible","finitely based","weakly Ramsey","orderly term","orderly composition"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]},{"key":"dc:rights","label":"Dc Rights","values":["unrestricted","This thesis or dissertation is protected by copyright: all rights reserved. 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We conclude by studying a class of Ramsey spaces, which arise from Ramsey algebras."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf","p.101","639. KB"]},{"key":"dc:title","label":"Title","values":["Ramsey Algebras and Ramsey Spaces"]}]}],"canonical_facts":{"dc:contributor":["Carlson, Timothy"],"dc:creator":["Teh, Wen Chean"],"dc:date":["2013-05-21"],"dc:description":["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."],"dc:format":["application/pdf","p.101","639. KB"],"dc:identifier":["http://rave.ohiolink.edu/etdc/view?acc_num=osu1357244115"],"dc:language":["English"],"dc:publisher":["The Ohio State University / OhioLINK"],"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."],"dc:subject":["Mathematics","Ramsey algebra","Ramsey space","reduction","idempotent ultrafilter","strongly reductible","finitely based","weakly Ramsey","orderly term","orderly composition"],"dc:title":["Ramsey Algebras and Ramsey Spaces"],"dc:type":["Electronic Thesis or Dissertation"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Doctor of Philosophy"],"thesis:institution_name":["The Ohio State University"]},"updated_at":"2026-07-24T03:36:08Z"}