Dartmouth Logic Seminar

Spring 2008

Seminar this term is Tuesdays at 2:00 pm in Kemeny 105.

Apr 8
Joe Mileti
Dartmouth College
Randomness and trees of positive measure
Apr 15
Joe Mileti
Dartmouth College
The reverse mathematics of weak versions of Ramsey's Theorem for pairs
Apr 22
No Seminar
Apr 29
Rebecca Weber
Dartmouth College
Definability and Invariance

A collection of computably enumerable Turing degrees is called invariant if it corresponds to a collection of c.e. sets which are invariant in the usual sense, under automorphisms of the lattice of all c.e. sets. A sweeping definability result by Cholak and Harrington gives the degree invariance of a large number of classes of degrees: the high_n and non-low_n degrees for every n > 1. Another standard structure in computability theory is the lattice of Pi^0_1 classes, or sets of infinite paths through computable trees. Currently there is only one known degree invariant class in the Pi^0_1 classes. We will discuss the status quo and an in-progress translation of the Cholak/Harrington result to a substructure of the lattice of Pi^0_1 classes, with consequences for the lattice as a whole.
May 6
Peter Barendse
Boston University
Regressive Partition Relations

RPRs are a combinatorial sort of large cardinal axioms. We will look at how they achieve transcendence and how they relate to better-known combinatorial large cardinal axioms.
May 13
Jared Corduan
Dartmouth College
Building a recursive tree with a unique infinite path of high complexity