Spring 2008
Seminar this term is Tuesdays at 2:00 pm in Kemeny 105.
| Date | Speaker | Title |
|---|---|---|
| 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 |