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


Title: Building Models of Strongly Minimal Theories - Part 1
Zoom link for remote attendance: https://uwmadison.zoom.us/j/96168027763?pwd=bGdvL3lpOGl6QndQcG5RTFUzY3JXQT09 (Meeting ID: 961 6802 7763, Password: 975f23)


Abstract: Since I'm talking in the Tuesday seminar as well, I'll use
=== January 29 - Organizational Meeting ===
the Monday seminar talk to do some background on the topic and some
lemmas that will go into the proofs in Tuesday's talk. There will be
(I hope) some theorems of interest to see on both days, and both on
the general topic of answering the following question: What do you
need to know about a strongly minimal theory in order to compute
copies of all of its countable models. I'll start with a definition
for strongly minimal theories and build up from there.


=== February 12, James Hanson ===
Steffen Lempp will give an overview and present some very basic forcing construction.


Title: Finding Definable Sets in Continuous Logic
We will then assign speakers to dates and topics.


Abstract: In order to be useful the notion of a 'definable set' in
=== '''February 5 - Taeyoung Em''' ===
continuous logic is stricter than a naive comparison to discrete logic
'''Title:''' Introduction to forcing
would suggest. As a consequence, even in relatively tame theories
there can be very few definable sets. For example, there is a
superstable theory with no non-trivial definable sets. As we'll see,
however, there are many definable sets in omega-stable,
omega-categorical, and other small theories.


=== February 19, Noah Schweber ===
'''Abstract:''' We introduce new definitions and properties regarding forcing.


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


Abstract: Although a given forcing notion may have nice properties on
'''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.
its own, those properties might vanish when we apply it repeatedly.
Early preservation results (that is, theorems saying that the
iteration of forcings with a nice property retains that nice property)
were fairly limited, and things really got off the ground with
Shelah's invention of "proper forcing." Roughly speaking, a forcing is
proper if it can be approximated by elementary submodels of the
universe in a particularly nice way. I'll define proper forcing and
sketch some applications.  


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


Title: A survey of computable and constructive mathematics in economic history
'''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'.


=== March 5, Tamvana Makulumi ===
=== '''February 26 - Karthik Ravishankar''' ===
'''Title:''' The 3 element chain as an initial segment of the Turing Degrees


Title: Convexly Orderable Groups
'''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 12, Dan Turetsky (University of Notre Dame) ===
=== '''March 4 - Karthik Ravishankar''' ===
'''Title:''' Bushy Tree forcing and constructing a minimal degree which is DNC


Title: Structural Jump
'''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 19, Ethan McCarthy ===
=== '''March 11 - Josiah Jacobsen-Grocott''' ===
'''Title:''' A uniformly e-pointed tree on Baire space without dead ends that is not of cototal degree


Title: Networks and degrees of points in non-second countable spaces
'''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.


=== April 2, Wil Cocke ===
=== '''March 18 - Alice Vidrine''' ===
'''Title:''' There is no non-computable bi-introreducible set


Title: Characterizing Finite Nilpotent Groups via Word Maps
'''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.


Abstract: In this talk, we will examine a novel characterization of finite
=== '''April 1 - Hongyu Zhu''' ===
nilpotent groups using the probability distributions induced by word
'''Title:''' The Conservativeness of WKL_0 over RCA_0 for <math>\Pi_1^1</math>-formulas
maps. In particular we show that a finite group is nilpotent if and
only if every surjective word map has fibers of uniform size.


=== April 9, Tejas Bhojraj ===
'''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.


Title: Quantum Randomness


Abstract: I will read the paper by Nies and Scholz where they define a notion of
<!-- Template
algorithmic randomness for infinite sequences of quantum bits
(qubits). This talk will cover the basic notions of quantum randomness
on which my talk on Tuesday will be based.


=== April 16, [http://www.math.wisc.edu/~ongay/ Iván Ongay-Valverde] ===
=== '''September 18 - xxx''' ===
'''Title:''' TBA ([https://wiki.math.wisc.edu/images/***.pdf Slides])


Title: What can we say about sets made by the union of Turing equivalence classes?
'''Abstract:''' TBA


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.
== Previous Years ==


This is a work in progress, so this talk will have multiple open questions and opportunities for feedback and public participation (hopefully).
The schedule of talks from past semesters can be found [[Graduate Logic Seminar, previous semesters|here]].
 
=== April 23, [http://www.math.wisc.edu/~mccarthy/ Ethan McCarthy] (Thesis Defense) ===
 
Title: TBA
 
Abstract: TBA
 
=== April 30, [http://www.math.uconn.edu/~westrick/ Linda Brown Westrick] (from University Of Connecticut) ===
 
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.