Ramsey theory and its application

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Zhao, Min

Contributors dc:contributor

• Solecki, Slawomir
• van den Dries, Lou
• Jockusch, Carl
• Hieronymi, Philipp

• Ramsey theory
• abstract Ramsey theorem
• Parameter system
• Self-Dual
• Partial order
• Linear order
• Interpretation

Statement dc:rights

• Copyright 2014 Min Zhao

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/72752

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/72752