2026-09-22T02:48:15Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/72752 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Solecki, Slawomir van den Dries, Lou Solecki, Slawomir Jockusch, Carl Hieronymi, Philipp Zhao, Min 2015-01-21T19:47:43Z 2015-01-21T19:47:43Z 2014-12 2015-01-21 2014-12 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. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2014-12-01T20:31:22Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 zhao_min.pdf: 692855 bytes, checksum: ae983031c85b472d70eedfb65e367995 (MD5) Made available in DSpace on 2015-01-21T19:47:43Z (GMT). No. of bitstreams: 1 Min_Zhao.pdf: 692848 bytes, checksum: 7ac9095d92f93ccc127adf9a1701854c (MD5) http://hdl.handle.net/2142/72752 en Copyright 2014 Min Zhao Ramsey theory abstract Ramsey theorem Parameter system Self-Dual Partial order Linear order Interpretation Ramsey theory and its application text Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD