Logic Seminar Abstracts


Title:  Park's Conjecture
Speaker:  Keith Kearnes
Affiliation:  CU
Time:  2pm, Tuesday, September 10
Location:  Math 220

Abstract:  
I will talk about the conjecture that a variety of algebras with a finite residual bound is finitely axiomatizable.


Title:  The Pixley problem
Speaker:  Keith Kearnes
Affiliation:  CU
Time:  2pm, Tuesday, September 24
Location:  Math 220

Abstract:  
Alden Pixley asked in 1984 whether a congruence distributive variety in a finite language can have infinitely many subdirectly irreducible algebras, all finite. I will talk about the negative answer to this question.


Title:  Survey on the structure of the Tukey theory of ultrafilters
Speaker:  Natasha Dobrinen
Affiliation:  DU
Time:  2pm, Tuesday, October 1
Location:  Math 220

Abstract:  
The Tukey order on ultrafilters is a weakening of the well-studied Rudin-Keisler order, and the exact relationship between them is a question of interest. In a second vein, Isbell showed that there is a maximum Tukey type among ultrafilters and asked whether there are others. These two questions are the main guiding forces of the current research. In this talk, we present highlights of recent work of Blass, Dobrinen, Mijares, Milovich, Raghavan, Todorcevic, and Trujillo (in various combinations for various papers). Further information about results mentioned in this talk can be found in a recent survey article by the speaker.


Title:  Dualizable algebras
Speaker:  Agnes Szendrei
Affiliation:  CU
Time:  2pm, Tuesday, October 8
Location:  Math 220

Abstract:  
Let A be a finite algebra in a residually small variety with a cube term. I will discuss sufficient conditions which ensure that A is dualizable.


Title:  Modal logics, coalgebraically
Speaker:  H. Peter Gumm
Affiliation:  Philipps-University, Marburg
Time:  2pm, Tuesday, November 12
Location:  Math 220

Abstract:  



Title:  Finitely related algebras
Speaker:  Alexandr Kazda
Affiliation:  Vanderbilt University
Time:  2pm, Tuesday, December 10
Location:  Math 220

Abstract:  
A finite algebra A is finitely related if we can obtain the clone of A as an algebra of polymorphisms of some finite relational structure, ie. there exist (finitary) relations R1,…,Rn such that the set of terms of A is precisely the set of operations that preserve all of R1,…,Rn. We will talk about a Summer job that involved determining which graph algebras are finitely related and about one curious conjecture linking finitely related algebras to absorption.




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