The Logic Seminar will meet again this Friday, usual place and time. The speaker will be Jack Yoon.
Title: Proof Mining
Abstract: Proof mining (proof unwinding) is a technique used to extract
constructive information from seemingly non-constructive proofs. We
discuss the idea behind the topic and describe the foundations which
form the basis for proof mining.
Jack Yoon will continue his explication of Proof Mining.
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.
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.
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).
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.
Continuation of last week’s talk
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.