{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/72752"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/72752","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Ramsey theory and its application","abstract":"In this dissertation, we study three problems about Ramsey theory. First, we prove a self-dual Ramsey theorem for parameter systems which is a generalization of the self-dual Ramsey theorem developed by Solecki. Second, we prove a Ramsey theorem for finite sets equipped with a partial order and a fixed number of linear orders extending the partial order. 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