Dartmouth Logic Seminar

Spring 2011

This term we are holding two seminar series. On Monday we will have the research-level seminar, and on Tuesday we will have an introductory-level seminar. All are welcome.

Introductory Logic Seminar

Tuesdays, 2:10-3:10 pm in 120 Kemeny Hall.

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, 2-3 pm in 120 Kemeny Hall.

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 d-computably 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 d-computably categorical. We also prove analogous results, one jump lower, for computable fields with splitting algorithms.