Date of Award

Spring 1-1-2016

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

First Advisor

Agnes Szendrei

Second Advisor

Peter Mayr

Third Advisor

Keith Kearnes

Fourth Advisor

Don Monk

Fifth Advisor

Fabio Somenzi

Abstract

The random permutation is the Fraïssé limit of the class of finite structures with two linear orders. Using a recent Ramsey-theoretic technique, we determine 13 finitary operations which generate the minimal polymorphism clones containing the automorphism group of the random permutation; we call such operations minimal functions. We also show that every reduct of the random permutation is model-complete and, answering a problem stated by Peter Cameron in 2002, we prove that there are 39 closed groups containing the automorphism group of the random permutation.

Included in

Mathematics Commons

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