Logic Seminar Abstracts


Title:  Chains in homomorphic images of some special Boolean algebras
Speaker:  Don Monk
Affiliation:  CU
Time:  3pm, Monday, March 15
Location:  Math 220

Abstract:  
We consider the Boolean algebra of subsets of an infinite cardinal κ which are of size less than λ or whose complement is of size less than λ. A complete characterization of what can happen to the supremum of sizes of chains in homomorphic images of such algebras is given.  


Title: Clones of finite groups are finitely related.
Speaker:  Kearnes
Affiliation:  CU
Time:   3pm, Monday, March 29
Location:   Math 220

Abstract:  
I'll prove a theorem of Aichinger, Mayr and McKenzie which implies that if G is a finite group, then there is a single finitary relation R on G such that a function w:Gn → G is representable by a group word iff it preserves R.



Title: Clones of finite groups are finitely related.
Speaker:  Kearnes
Affiliation:  CU
Time:   3pm, Monday, April 5
Location:   Math 220

Abstract:  
Continuation.



Title: A completeness criterion for Słupecki's clone
Speaker:  Ágnes Szendrei
Affiliation:  CU
Time:   3pm, Monday, April 12
Location:   Math 220

Abstract:  
Słupecki's clone consists of all essentially unary operations and all nonsurjective operations on some finite set. I will prove a completeness theorem for this clone by showing that any clone that fails to contain all nonsurjective operations is compatible with a relation from one of eight different families of relations.



Title: A completeness criterion for Słupecki's clone
Speaker:  Ágnes Szendrei
Affiliation:  CU
Time:   3pm, Monday, April 19
Location:   Math 220

Abstract:  
Continuation.



Title: Some key theorems about the structure of Tukey types of ultrafilters
Speaker:  Natasha Dobrinen
Affiliation:  Denver University
Time:   3pm, Monday, April 26
Location:   Math 220

Abstract:  
We will present an overview of structure theorems of Tukey types of ultrafilters and compare and contrast this with the well-known structure theorems for Rudin-Keisler equivalence classes of ultrafilters.





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