Logic Seminar Abstracts


Title:  A new proof of Baker's Finite Basis Theorem
Speaker:  Keith Kearnes
Affiliation:  CU
Time:  3pm, Monday, January 27
Location:  Math 220

Abstract:  
In 1971, Kirby Baker proved that a finitely generated congruence distributive variety in a finite language is finitely axiomatizable. A number of proofs of this theorem have been given since then, and in this talk we present the most recentone: a proof by Baker and Ju Wang.


Title:  A new proof of Baker's Finite Basis Theorem
Speaker:  Kearnes
Affiliation:  CU
Time:  3pm, Monday, February 3
Location:  Math 220

Abstract:  
A continuation of the previous talk.


Title:  A new proof of Baker's Finite Basis Theorem
Speaker:  Kearnes
Affiliation:  CU
Time:  3pm, Monday, February 10
Location:  Math 220

Abstract:  
A continuation of the previous talk.


Title:  The Shape of Congruence Lattices
Speaker:  Keith Kearnes
Affiliation:  CU
Time:  3pm, Monday, March 10
Location:  Math 220

Abstract:  
In this sequence of talks we discuss relationships between term conditions, Maltsev conditions, and the shapes of congruence lattices in a variety of algebras.


Title:  The Shape of Congruence Lattices
Speaker:  Kearnes
Affiliation:  CU
Time:  3pm, Monday, March 17
Location:  Math 220

Abstract:  
A continuation of the previous talk.


Title:  The Nesting of Sentential Formulas
Speaker:  Sid Smith
Affiliation:  CU
Time:  3pm, Monday, April 14
Location:  Math 220

Abstract:  
Suppose G is a sentential formula in the propositional variables a_1,...,a_n,b_1,...,b_m. We say that G is nestable for the given choice of the b's if there is a sentential formula B(b_1,...,b_m) and a sentential formula A(a_1,...,a_n,B) such that A is equivalent to G. Sufficient and necessary conditions for the existence of a given nesting are proved, and an algorithm is given.


Title:  The Number of Aut(L)-Orbits of an Infinite Field L
Speaker:  Kearnes
Affiliation:  CU
Time:  3pm, Monday, April 21
Location:  Math 220

Abstract:  
It has long been known that there exist infinite division rings D such that Aut(D) has exactly three orbits: {0}, {1}, and D-{0,1}. Until recently it was (apparently) unknown whether there is an infinite field with finitely many orbits under its automorphism group. I will give a proof that there is no such field. The proof combines contributions from George Bergman, KK, Kiran Kedlaya, Hendrick Lenstra, Bjorn Poonen, and Thomas Scanlon.


Title:  The Number of Aut(L)-Orbits of an Infinite Field L
Speaker:  Kearnes
Affiliation:  CU
Time:  3pm, Monday, April 28
Location:  Math 220

Abstract:  
A continuation of the previous talk.



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