Graduate Logic Seminar: Difference between revisions

From UW-Math Wiki
Jump to navigation Jump to search
(The Graduate Logic Seminar is an informal space where graduate student and professors present topics related to logic which are not necessarly original or completed work. This is an space focus principally in practicing presentation skills or learning ma)
 
(235 intermediate revisions by 11 users not shown)
Line 1: Line 1:
The Graduate Logic Seminar is an informal space where graduate student and professors present topics related to logic which are not necessarly original or completed work. This is an space focus principally in  practicing presentation skills or learning materials that are not usually presented on a class.
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, 4:00 PM – 5:00 PM (unless otherwise announced).
* '''When:''' Mondays 3:30-4:30 PM
* '''Where:''' Van Vleck B235 (unless otherwise announced).
* '''Where:''' Van Vleck B223
* '''Organizers:''' [https://www.math.wisc.edu/~msoskova/ Mariya Soskava]
* '''Organizers:''' [https://people.math.wisc.edu/~slempp/ Steffen Lempp] and [https://sites.google.com/view/hongyu-zhu/ Hongyu Zhu]


Talks schedule are arrange and decide at the beginning of each semester. If you would like to participate, please contact one of the organizers.
The talk schedule is arranged at the beginning of each semester. If you would like to participate, please contact one of the organizers.


== Spring 2018 ==
Sign up for the graduate logic seminar mailing list:  [mailto:join-grad-logic-sem@lists.wisc.edu join-grad-logic-sem@lists.wisc.edu]


=== January 29, Organizational meeting ===
== Spring 2024 ==


This day we decided the schedule for the semester.
The seminar will be run as a 1-credit seminar Math 975 . In Spring 2024, the topic will be forcing constructions in computability theory. If you are not enrolled but would like to audit it, please contact [https://people.math.wisc.edu/~slempp/ Steffen Lempp]  and [mailto:hongyu@math.wisc.edu Hongyu Zhu].


=== February 5, (person) ===
Presentation Schedule: https://docs.google.com/spreadsheets/d/1JC6glG_soNLtaMQWaAuADlUu8dh2eJ0NL-MaUr7-nOk/edit?usp=sharing


Title:  
Zoom link for remote attendance: https://uwmadison.zoom.us/j/96168027763?pwd=bGdvL3lpOGl6QndQcG5RTFUzY3JXQT09 (Meeting ID: 961 6802 7763, Password: 975f23)


Abstract:
=== January 29 - Organizational Meeting ===


=== February 12, (Person) ===
Steffen Lempp will give an overview and present some very basic forcing construction.


Title:
We will then assign speakers to dates and topics.


Abstract:  
=== '''February 5 - Taeyoung Em''' ===
'''Title:''' Introduction to forcing


=== February 19, (Person) ===
'''Abstract:''' We introduce new definitions and properties regarding forcing.


Title:  
=== '''February 12 - Hongyu Zhu''' ===
'''Title:''' Slaman-Woodin Forcing and the Theory of Turing Degrees


Abstract:  
'''Abstract:''' We will discuss how to use Slaman-Woodin forcing to interpret true second(first, resp.)-order arithmetic in the Turing degrees (Turing degrees below 0', resp.), thereby showing they have the same Turing degree.


=== February 26, (Person) ===
=== '''February 19 - John Spoerl''' ===
'''Title:''' Forcing with Trees - Spector's and Sack's Minimal Degrees


Title:  
'''Abstract:''' We'll take a look at Spector's forcing which uses perfect trees as conditions.  Then we'll see where we might make some improvements which leads to Sack's sharpening of Spector's theorem: there is a minimal degree below 0'.


Abstract:  
=== '''February 26 - Karthik Ravishankar''' ===
'''Title:''' The 3 element chain as an initial segment of the Turing Degrees


=== March 5, (Person) ===
'''Abstract:''' In this talk, we'll look at the construction of a minimal degree with a strong minimal cover which shows that the three-element chain can be embedded as an initial segment of the Turing Degrees. The construction builds off ideas of Spector's minimal degree with stronger assumptions on the forcing conditions used. If time permits, we'll also talk about Copper's Jump Inversion building off Sack's construction.


Title:  
=== '''March 4 - Karthik Ravishankar''' ===
'''Title:''' Bushy Tree forcing and constructing a minimal degree which is DNC


Abstract:  
'''Abstract:''' We shall look at a forcing technique called Bushy Tree forcing using it to show that there is no uniform way to compute a DNC_2 from a DNC_3 function and that there is a DNC function that is weak in the sense that it does not compute a computably bounded DNC function. We present a few other results along these lines and sketch the construction of a minimal degree that is DNC relative to any given oracle using bushy tree forcing.


=== March 12, (Person) ===
=== '''March 11 - Josiah Jacobsen-Grocott''' ===
'''Title:''' A uniformly e-pointed tree on Baire space without dead ends that is not of cototal degree


Title:  
'''Abstract:''' A set is cototal if it is enumeration reducible to its complement. A tree is e-point if every path on the tree can enumerate the tree. McCathy proved that these notions are equivalent up to e-degree when considering e-pointed trees on cantor space. This fails when considering trees on Baire space. We give an example of a simple forcing construction that produces e-pointed trees on Baire space. We carefully analyze this forcing partial order to prove that generic e-pointed trees without dead ends are not of cototal degree.


Abstract:  
=== '''March 18 - Alice Vidrine''' ===
'''Title:''' There is no non-computable bi-introreducible set


=== March 19, (Person) ===
'''Abstract:''' A set is said to be bi-introreducible if it can be computed by any of its infinite subsets, or any infinite subset of its complement. This talk will detail a Matthias forcing construction used to prove a theorem by Seetapun which implies that the bi-introreducible sets are exactly the computable sets.


Title:  
=== '''April 1 - Hongyu Zhu''' ===
'''Title:''' The Conservativeness of WKL_0 over RCA_0 for <math>\Pi_1^1</math>-formulas


Abstract:  
'''Abstract:''' We will see how to use forcing to construct models of WKL_0 from models of RCA_0 while preserving certain arithmetical truths, thereby showing that WKL_0 is <math>\Pi_1^1</math>-conservative over RCA_0.


=== April 2, (Person) ===


Title:
<!-- Template


Abstract:  
=== '''September 18 - xxx''' ===
'''Title:''' TBA ([https://wiki.math.wisc.edu/images/***.pdf Slides])


=== April 9, (Person) ===
'''Abstract:''' TBA


Title:
-->


Abstract:
== Previous Years ==


=== April 16, Iván Ongay-Valverde ===
The schedule of talks from past semesters can be found [[Graduate Logic Seminar, previous semesters|here]].
 
Title: What can we say about sets made by the union of Turing equivalence classes?
 
Abstract: It is well known that given a real number x (in the real line) the set of all reals that have the same Turing degree (we will call this a Turing equivalence class) have order type 'the rationals' and that, unless x is computable, the set is not a subfield of the reals. Nevertheless, what can we say about the order type or the algebraic structure of a set made by the uncountable union of Turing equivalence classes?
 
This topic hasn't been deeply studied. In this talk I will focus principally on famous order types and answer whether they can be achieved or not. Furthermore, I will explain some possible connections with the automorphism problem of the Turing degrees.
 
This is a work in progress, so this talk will have multiple open questions and opportunities for feedback and public participation (hopefully).
 
=== April 23, Ethan (Defense) ===
 
Title: TBA
 
Abstract: TBA
 
=== April 30, Linda ===
 
Title: TBA
 
Abstract: TBA
 
=== May 7, TBA ===
 
Title: TBA
 
Abstract: TBA
 
== Fall 2017 ==
 
=== September 11, Organizational meeting ===
 
This day we decided the schedule for the semester.
 
=== September 18, (person) ===
 
Title:
 
Abstract:
 
=== September 25, (Person) ===
 
Title:
 
Abstract:
 
=== October 2, (Person) ===
 
Title:
 
Abstract:
 
=== October 9, (Person) ===
 
Title:
 
Abstract:
 
=== October 16, (Person) ===
 
Title:
 
Abstract:
 
=== October 23, (Person) ===
 
Title:
 
Abstract:
 
=== October 30, Iván Ongay-Valverde ===
 
Title:
 
Abstract:
 
=== November 6, (Person) ===
 
Title:
 
Abstract:
 
=== November 13, (Person) ===
 
Title:
 
Abstract:
 
=== November 20, (Person) ===
 
Title:
 
Abstract:
 
=== November 27, (Person) ===
 
Title: TBA
 
Abstract: TBA
 
=== December 4, (Person) ===
 
Title: TBA
 
Abstract: TBA
 
=== December 11, (Person) ===
 
Title: TBA
 
Abstract: TBA
 
==Previous Years==
 
The schedule of talks from past semesters can be found [[Logic Graduate Seminar, previous semesters|here]].

Latest revision as of 22:43, 27 March 2024

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.

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

Spring 2024

The seminar will be run as a 1-credit seminar Math 975 . In Spring 2024, the topic will be forcing constructions in computability theory. If you are not enrolled but would like to audit it, please contact Steffen Lempp and Hongyu Zhu.

Presentation Schedule: https://docs.google.com/spreadsheets/d/1JC6glG_soNLtaMQWaAuADlUu8dh2eJ0NL-MaUr7-nOk/edit?usp=sharing

Zoom link for remote attendance: https://uwmadison.zoom.us/j/96168027763?pwd=bGdvL3lpOGl6QndQcG5RTFUzY3JXQT09 (Meeting ID: 961 6802 7763, Password: 975f23)

January 29 - Organizational Meeting

Steffen Lempp will give an overview and present some very basic forcing construction.

We will then assign speakers to dates and topics.

February 5 - Taeyoung Em

Title: Introduction to forcing

Abstract: We introduce new definitions and properties regarding forcing.

February 12 - Hongyu Zhu

Title: Slaman-Woodin Forcing and the Theory of Turing Degrees

Abstract: We will discuss how to use Slaman-Woodin forcing to interpret true second(first, resp.)-order arithmetic in the Turing degrees (Turing degrees below 0', resp.), thereby showing they have the same Turing degree.

February 19 - John Spoerl

Title: Forcing with Trees - Spector's and Sack's Minimal Degrees

Abstract: We'll take a look at Spector's forcing which uses perfect trees as conditions. Then we'll see where we might make some improvements which leads to Sack's sharpening of Spector's theorem: there is a minimal degree below 0'.

February 26 - Karthik Ravishankar

Title: The 3 element chain as an initial segment of the Turing Degrees

Abstract: In this talk, we'll look at the construction of a minimal degree with a strong minimal cover which shows that the three-element chain can be embedded as an initial segment of the Turing Degrees. The construction builds off ideas of Spector's minimal degree with stronger assumptions on the forcing conditions used. If time permits, we'll also talk about Copper's Jump Inversion building off Sack's construction.

March 4 - Karthik Ravishankar

Title: Bushy Tree forcing and constructing a minimal degree which is DNC

Abstract: We shall look at a forcing technique called Bushy Tree forcing using it to show that there is no uniform way to compute a DNC_2 from a DNC_3 function and that there is a DNC function that is weak in the sense that it does not compute a computably bounded DNC function. We present a few other results along these lines and sketch the construction of a minimal degree that is DNC relative to any given oracle using bushy tree forcing.

March 11 - Josiah Jacobsen-Grocott

Title: A uniformly e-pointed tree on Baire space without dead ends that is not of cototal degree

Abstract: A set is cototal if it is enumeration reducible to its complement. A tree is e-point if every path on the tree can enumerate the tree. McCathy proved that these notions are equivalent up to e-degree when considering e-pointed trees on cantor space. This fails when considering trees on Baire space. We give an example of a simple forcing construction that produces e-pointed trees on Baire space. We carefully analyze this forcing partial order to prove that generic e-pointed trees without dead ends are not of cototal degree.

March 18 - Alice Vidrine

Title: There is no non-computable bi-introreducible set

Abstract: A set is said to be bi-introreducible if it can be computed by any of its infinite subsets, or any infinite subset of its complement. This talk will detail a Matthias forcing construction used to prove a theorem by Seetapun which implies that the bi-introreducible sets are exactly the computable sets.

April 1 - Hongyu Zhu

Title: The Conservativeness of WKL_0 over RCA_0 for [math]\displaystyle{ \Pi_1^1 }[/math]-formulas

Abstract: We will see how to use forcing to construct models of WKL_0 from models of RCA_0 while preserving certain arithmetical truths, thereby showing that WKL_0 is [math]\displaystyle{ \Pi_1^1 }[/math]-conservative over RCA_0.


Previous Years

The schedule of talks from past semesters can be found here.