Logic Seminar Abstracts


Title:  Separating Notions of Randomness
Speaker:  Bart Kastermans
Affiliation:  University of Wisconsin
Time:  10am, Thursday, January 15
Location:  Math 220

Abstract:  
Mathematicians often have an intuitive idea about which real numbers are random and what properties they should satisfy. These intuitions differ between mathematicians. We'll explain some of these, and how they give rise to several different formalizations of randomness. The situation is similar to the idea about area, which can be formalized by different integrals.

Having different formalizations related to one intuition raises the question of which parts of these formalizations are essential and which are formal noise (e.g., how are the different formalizations related?).

We'll explain several formalizations using the idea of martingales, and give some of the ideas involved in separating permutation and injective randomness from Martin-Lof randomness. This is related to the question of separating Kolmogorov-Loveland randomness from Martin-Lof randomness.  


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