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Ramsey theory and its application
Zhao, Min
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https://hdl.handle.net/2142/72752
Description
- Title
- Ramsey theory and its application
- Author(s)
- Zhao, Min
- Issue Date
- 2015-01-21
- Director of Research (if dissertation) or Advisor (if thesis)
- Solecki, Slawomir
- Doctoral Committee Chair(s)
- van den Dries, Lou
- Committee Member(s)
- Solecki, Slawomir
- Jockusch, Carl
- Hieronymi, Philipp
- Department of Study
- Mathematics
- Discipline
- Mathematics
- Degree Granting Institution
- University of Illinois at Urbana-Champaign
- Degree Name
- Ph.D.
- Degree Level
- Dissertation
- Date of Ingest
- 2015-01-21T19:47:43Z
- Keyword(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.
- Graduation Semester
- 2014-12
- Permalink
- http://hdl.handle.net/2142/72752
- Copyright and License Information
- Copyright 2014 Min Zhao
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