Graduate Logic Seminar: Difference between revisions
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'''Abstract:''' We will go over briefly some basic information about trees and infinite games. Then we prove the Gale-Stewart Theorem. The proof of the theorem motivates definition of quasistrategy. Then we will briefly introduce Borel determinacy. We will go over how the usage of A.C. makes convenient for us to make a non-quasidetermined or undertermined game. We will give an explicit construction of a non-quasidetermined game on <math>\mathcal P(2^{\mathbb N})</math> without using A.C. | '''Abstract:''' We will go over briefly some basic information about trees and infinite games. Then we prove the Gale-Stewart Theorem. The proof of the theorem motivates definition of quasistrategy. Then we will briefly introduce Borel determinacy. We will go over how the usage of A.C. makes convenient for us to make a non-quasidetermined or undertermined game. We will give an explicit construction of a non-quasidetermined game on <math>\mathcal P(2^{\mathbb N})</math> without using A.C. | ||
=== '''September 25 - Karthik Ravishankar''' === | |||
'''Title:''' Spectra of structures | |||
'''Abstract:''' One way to measure the complexity of a structure is via its spectrum - the set of Turing degrees of its copies. In this talk, we'll look at the definition and first properties of the spectrum followed by some examples. In particular, we'll show that the non-computable degrees and the hyperimmune degrees form a spectrum while the DNC degrees do not. | |||
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Revision as of 15:05, 23 September 2023
The Graduate Logic Seminar is an informal space where graduate students and professors present topics related to logic which are not necessarily original or completed work. This is a space focused principally on practicing presentation skills or learning materials that are not usually presented in a class.
- When: Mondays 3:30-4:30 PM
- Where: Van Vleck B223
- Organizers: Uri Andrews and Hongyu Zhu
The talk schedule is arranged at the beginning of each semester. If you would like to participate, please contact one of the organizers.
Sign up for the graduate logic seminar mailing list: join-grad-logic-sem@lists.wisc.edu
Fall 2023
The seminar will be run as a 1-credit seminar Math 975 in Fall 2023. If you are not enrolled but would like to audit it, please contact Uri Andrews and Hongyu Zhu.
While you are welcome (and encouraged) to present on a topic of your own choice, feel free to ask for help from faculties and/or other graduate students.
Presentation Schedule: https://docs.google.com/spreadsheets/d/15Qd4EzrrKpn1Ct5tur1P_FDc2czsdAVnUf_pfp65Lb4/edit?usp=sharing
Zoom link for remote attendance: https://uwmadison.zoom.us/j/96168027763?pwd=bGdvL3lpOGl6QndQcG5RTFUzY3JXQT09 (Meeting ID: 961 6802 7763, Password: 975f23)
Possible readings:
- (Elementary) Proof Theory: Chapters 4-7 of Aspects of Incompleteness by Per Lindström.
- An invitation to model-theoretic Galois theory. On arxiv here.
- Variations on the Feferman-Vaught Theorem On arxiv here.
- Any of several papers on "Turing Computable Embeddings"
- Computability/Model/Set Theory: Consult faculties/students for recommended texts on specific areas.
September 11 - Organizational Meeting
We will meet to assign speakers to dates.
September 18 - Taeyoung Em
Title: Explicit construction of non-quasidetermined game on [math]\displaystyle{ \mathcal P(2^{\mathbb N}) }[/math] without using A.C. (Supplement)
Abstract: We will go over briefly some basic information about trees and infinite games. Then we prove the Gale-Stewart Theorem. The proof of the theorem motivates definition of quasistrategy. Then we will briefly introduce Borel determinacy. We will go over how the usage of A.C. makes convenient for us to make a non-quasidetermined or undertermined game. We will give an explicit construction of a non-quasidetermined game on [math]\displaystyle{ \mathcal P(2^{\mathbb N}) }[/math] without using A.C.
September 25 - Karthik Ravishankar
Title: Spectra of structures
Abstract: One way to measure the complexity of a structure is via its spectrum - the set of Turing degrees of its copies. In this talk, we'll look at the definition and first properties of the spectrum followed by some examples. In particular, we'll show that the non-computable degrees and the hyperimmune degrees form a spectrum while the DNC degrees do not.
Previous Years
The schedule of talks from past semesters can be found here.