Spring 2011
This term we are holding two seminar series. On Monday we will have the researchlevel seminar, and on Tuesday we will have an introductorylevel seminar. All are welcome.
Introductory Logic Seminar
Tuesdays, 2:103:10 pm in 120 Kemeny Hall.
Date  Speaker  Title 

Apr 5  Seth Harris  Set Theory: introduction to Suslin's problem 
Apr 12  Seth Harris  Set Theory: Martin's axiom 
Apr 19  Cancelled  
Apr 26  Marcia Groszek  The constructible universe and the continuum hypothesis 
May 3  Cancelled  
May 10  Marcia Groszek  More on the constructible universe 
Logic Seminar
Mondays, 23 pm in 120 Kemeny Hall.
Date  Speaker  Title 

Apr 4 
Johanna Franklin
Dartmouth College

Extending difference randomness 1 
Apr 11 
Johanna Franklin
Dartmouth College

Extending difference randomness 2 
Apr 18 
Rebecca Weber
Dartmouth College

Effective dimension Hausdorff dimension may be defined in terms of betting in inflationary environments. By restricting the class of betting strategies (a form of martingales) used, an effective form of dimension arises in which individual points may have dimension greater than 0. Effective dimension also may be characterized in terms of Kolmogorov complexity. 
Apr 25 
Rebecca Weber
Dartmouth College

Lowness for dimension When dimension is viewed in terms of betting functions, those functions may be given oracles. A point that does not decrease the dimension of any other points when used as an oracle is called low for dimension. Recent joint work has produced a list of equivalent characterizations of points that are low for dimension in terms of Kolmogorov complexity and other properties. 
May 2 
Russell Miller
Queens College, CUNY

in Kemeny 004 Degrees of Categoricity of Algebraic Fields Let F be a computable field: a countable field in which the addition and multiplication are given by computable functions. We investigate the Turing degrees d such that F is dcomputably categorical, meaning that d is able to compute isomorphisms between F and every other computable field isomorphic to F. We prove that algebraic fields can fail to be 0'computably categorical, but that there is a degree d, low relative to 0', such that every algebraic field is dcomputably categorical. We also prove analogous results, one jump lower, for computable fields with splitting algorithms. 