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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 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:''' Tuesdays 4-5 PM
* '''When:''' Mondays 3:30-4:30 PM
* '''Where:''' Van Vleck 901
* '''Where:''' Van Vleck B223
* '''Organizers:''' [https://www.math.wisc.edu/~jgoh/ Jun Le Goh]
* '''Organizers:''' [https://people.math.wisc.edu/~slempp/ Steffen Lempp] and [https://sites.google.com/view/hongyu-zhu/ 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.
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
Sign up for the graduate logic seminar mailing list:  [mailto:join-grad-logic-sem@lists.wisc.edu join-grad-logic-sem@lists.wisc.edu]


== Fall 2021 tentative schedule ==
== Spring 2024 ==


To see what's happening in the Logic qual preparation sessions click [[Logic Qual Prep|here]].
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].


=== September 14 - organizational meeting ===
Presentation Schedule: https://docs.google.com/spreadsheets/d/1JC6glG_soNLtaMQWaAuADlUu8dh2eJ0NL-MaUr7-nOk/edit?usp=sharing


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


=== September 28 - Ouyang Xiating ===
=== January 29 - Organizational Meeting ===


Title: First-order logic, database and consistent query answering
Steffen Lempp will give an overview and present some very basic forcing construction.


Abstract: Databases are a crucial component of many (if not all) modern
We will then assign speakers to dates and topics.
applications. In reality, the data stored are often dirty and contain
duplicated/missing entries, and it is a natural practice to clean the data
first before executing the query. However, the same query might return
different answers on different cleaned versions of the dataset. It is then
helpful to compute the consistent answers: the query answers that will always
be returned, regardless of how the dirty data is cleaned. In this talk, we
first introduce the connection between first-order logic and query languages
on databases, and then discuss the problem of Consistent Query Answering
(CQA): How to compute consistent answers on dirty data? Finally, we show
when the CQA problem can be solved using first-order logic for path queries.


=== October 12 - Karthik Ravishankar ===
=== '''February 5 - Taeyoung Em''' ===
'''Title:''' Introduction to forcing


Title: Notions of randomness for subsets of the Natural Numbers
'''Abstract:''' We introduce new definitions and properties regarding forcing.


Abstract: There are a number of notions of randomness of sets of natural numbers. These notions have been defined based on what a 'random object' should behave like such as being 'incompressible' or being 'hard to predict' etc. There is often a interplay between computability and randomness aspects of subsets of natural numbers. In this talk we motivate and present a few different notions of randomness and compare their relative strength.
=== '''February 12 - Hongyu Zhu''' ===
'''Title:''' Slaman-Woodin Forcing and the Theory of Turing Degrees


=== October 26 - no seminar ===
'''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.


=== November 9 - Antonio Nákid Cordero ===
=== '''February 19 - John Spoerl''' ===
'''Title:''' Forcing with Trees - Spector's and Sack's Minimal Degrees


Title: Martin's Conjecture: On the uniqueness of the Turing jump
'''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: The partial order of the Turing degrees is well-known to be extremely complicated. However, all the Turing degrees that appear "naturally" in mathematics turn out to be well-ordered. In the '70s, Martin made a sharp conjecture explaining this phenomenon, the prime suspect: the Turing jump. This talk will explore the precise statement of Martin's conjecture and the interesting mathematics that surround it.
=== '''February 26 - Karthik Ravishankar''' ===
'''Title:''' The 3 element chain as an initial segment of the Turing Degrees


=== November 23 - Antonio Nákid Cordero ===
'''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: Two Perspectives on Martin's Conjecture.
=== '''March 4 - Karthik Ravishankar''' ===
'''Title:''' Bushy Tree forcing and constructing a minimal degree which is DNC


Abstract: This time we will dive deeper into the recent developments around Martin's Conjecture. We will focus on two main themes: the uniformity assumption, and the interaction of Martin's conjecture with the theory of countable Borel equivalence relations.
'''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.


=== December 7 - John Spoerl ===
=== '''March 11 - Josiah Jacobsen-Grocott''' ===
'''Title:''' A uniformly e-pointed tree on Baire space without dead ends that is not of cototal degree


Title: Cardinals Beyond Choice and Inner Model Theory
'''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: This talk will be a general introduction and overview of large cardinal axioms which violate the axiom of choice and their impact on the project of inner model theory.
=== '''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>\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>\Pi_1^1</math>-conservative over RCA_0.
 
 
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=== '''September 18 - xxx''' ===
'''Title:''' TBA ([https://wiki.math.wisc.edu/images/***.pdf Slides])
 
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== Previous Years ==
== Previous Years ==


The schedule of talks from past semesters can be found [[Graduate Logic Seminar, previous semesters|here]].
The schedule of talks from past semesters can be found [[Graduate Logic 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.