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
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.
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