**Computational Logic Seminar**

** Tuesday, March 19, 2013 2:00 pm**

Speaker: Stan Wainer The Leeds Logic Group, University of Leeds

Title: Computing Bounds from Arithmetical Proofs

We explore the role of the function a+2^x, and its generalizations to

higher number classes, in analyzing and measuring the computational

content of a broad spectrum of arithmetical theories. Newer

formalizations of such theories, based on the well-known normal/safe

variable separation of Bellantoni-Cook, enable uniform

proof-theoretical treatments of poly-time arithmetics, through Peano

arithmetic, and up to finitely iterated inductive definitions.

**Models of PA**

** Wednesday, March 20, 2013 6:45 pm**

Speaker: Stan Wainer The Leeds Logic Group, University of Leeds

Title: Fast Growing Functions and Arithmetical Independence Results

We explore the role of the function $a+2^x$ and its generalisations to

higher number classes, in supplying complexity bounds for the provably

computable functions across a broad spectrum of (arithmetically based)

theories. We show how the resulting “fast growing” subrecursive

hierarchy forges direct links between proof theory and various

combinatorial independence results – e.g. Goodstein’s Theorem (for

Peano Arithmetic) and Friedman’s Miniaturised Kruskal Theorem for

Labelled Trees (for $Pi^1_1$-CA$_0$).

Ref: Schwichtenberg and Wainer, “Proofs and Computations”, Persp. in

Logic, CUP 2012.

**Set theory seminar**

** Friday, March 22, 2013 10:00 am**

Speaker: Kaethe Minden The CUNY Graduate Center

Title: Ramsey ultrafilters

I will introduce the concept of a Ramsey ultrafilter and show that

under Martin’s Axiom, and under the continuum hypothesis, Ramsey

ultrafilters exists. I will actually show that this follows from some

consequences of MA on cardinal invariants of the continuum. If time

permits, I will make a connection to Ramsey’s theorem. This talk is

intended to bridge the gap between the previous talk by Miha Habic on

Martin’s Axiom and the upcoming talks by Victoria Gitman on Ramsey

cardinals.

**CUNY Logic Workshop**

** Friday, March 22, 2013 2:00 pm**

Speaker: Peter Koepke Rheinische Friedrich-Wilhelms-Universität Bonn

Title: Namba-like singularizations of successor cardinals

Bukowski-Namba forcing preserves aleph_1 and changes the cofinality of

aleph_2 to omega. We lift this to cardinals kappa > aleph_1 :

Assuming a measurable cardinal lambda we construct models over which

there is a further “Namba-like” forcing which preserves all cardinals

<= kappa and changes the cofinality of kappa^+ to omega. Cofinalities

different from omega can also be achieved by starting from measurable

cardinals of sufficiently strong Mitchell order. Using core model

theory one can show that the respective measurable cardinals are also

necessary. This is joint work with Dominik Adolf (Münster).

**CUNY Logic Workshop**

** Friday, March 22, 2013 4:00 pm**

Speaker: Philip Welch University of Bristol

Title: Determinacy in analysis and beyond

Recently Montalban and Shore derived precise limits to the amount of

determinacy provable in second order arithmetic. We review some of

the results in this area and recent work on lifting this to a setting

of ZF^- with a single measurable cardinal.