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Title:Ramsey theory and its application
Author(s):Zhao, Min
Director of Research:Solecki, Slawomir
Doctoral Committee Chair(s):van den Dries, Lou
Doctoral Committee Member(s):Solecki, Slawomir; Jockusch, Carl; Hieronymi, Philipp
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Ramsey theory
abstract Ramsey theorem
Parameter system
Self-Dual
Partial order
Linear order
Interpretation
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. Third, we study the relations between Ramsey theorems which have points in common with the classical Ramsey theorem and the dual Ramsey theorem by the concept of interpretation.
Issue Date:2015-01-21
URI:http://hdl.handle.net/2142/72752
Rights Information:Copyright 2014 Min Zhao
Date Available in IDEALS:2015-01-21
Date Deposited:2014-12


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