Apr

28

Fri

Jack Yoon will continue his explication of Proof Mining.

May

5

Fri

David Webb will speak at 1:00-2:00 in Keller 402

Title: Every Function Can be Computable

Abstract: I will relay an interesting result of Joel David Hamkins: that

there is an algorithm which can compute any function f of natural

numbers, if it is carried out in the right model of arithmetic

(corresponding to f). In particular, I will construct the necessary

models using Rosser sentences and describe the algorithm.

Aug

31

Thu

This semester the Logic Seminar will meet on Thursdays, 2:50 – 3:40 pm in Keller 402.

This Thursday we will have a (probably brief) organizational meeting.

Title: Some nonstandard remarks about Egyptian fractions

Abstract: An Egyptian fraction is a finite sum of fractions of the form $1/n$, where $n$ is a natural number. I’ll give simple proofs of some results about such fractions (also about Znám fractions). The proofs only require the compactness theorem from first order logic, though I’ll use the language of nonstandard analysis.

Sep

14

Thu

Title: A Simple Proof of a Theorem of Woodin

Abstract: In a similar spirit as my talk last semester about computing

and non-standard models, I will relay Joel David Hamkins’ new proof of a

theorem of Woodin: that there is a function that enumerates any finite

set (if computed in the correct model M of arithmetic), and which can

enumerate any extension of that set (if run in the correct end-extension

of M).

Sep

21

Thu

Title: Measure-Risking Arguments in Recursion Theory

Abstract: By way of introducing the idea of measure-risking, I will present a proof of Kurtz’s theorem that the Turing upward closure of the set of 1-generic reals is of full Lebesgue measure. Then I will show how a stronger form of the theorem (due originally to Kautz) can be obtained by framing the proof as a “fireworks argument”, following a recent paper of Bienvenu and Patey.

Oct

5

Thu

Title: Borel Determinacy I

Speaker: Umar Gaffar

We’re going through Ross Bryant’s presentation of Martin’s theorem (in ZFC) that Borel games are determined.

## University of Hawaiʻi at Mānoa