Difference between revisions of "Graduate Logic Seminar"

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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.
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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.
  
* '''When:''' Mondays, 4:00 PM – 5:00 PM (unless otherwise announced).
+
* '''When:''' Tuesdays 4-5 PM
* '''Where:''' Van Vleck B235 (unless otherwise announced).
+
* '''Where:''' Van Vleck 901
* '''Organizers:''' [https://www.math.wisc.edu/~msoskova/ Mariya Soskava]
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* '''Organizers:''' [https://www.math.wisc.edu/~jgoh/ Jun Le Goh]
  
Talks schedule are arrange and decide at the beginning of each semester. If you would like to participate, please contact one of the organizers.
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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 ==
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Sign up for the graduate logic seminar mailing list:  join-grad-logic-sem@lists.wisc.edu
  
=== January 29, Organizational meeting ===
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== Spring 2022 ==
  
This day we decided the schedule for the semester.
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The graduate logic seminar this semester will be run as MATH 975. Please enroll if you wish to participate.
  
=== February 5, Uri Andrews ===
+
We plan to cover the first 9 parts of [https://blog.nus.edu.sg/matwong/teach/modelarith/ Tin Lok Wong's notes], as well as a few other relevant topics which are not covered in the notes:
 +
* Properness of the induction/bounding hierarchy (chapter 10 of Models of Peano Arithmetic by Kaye is a good source)
 +
* Tennenbaum's theorem (this is a quick consequence of the main theorem of part 4, so it should be combined with part 4 or part 5)
 +
* Other facts found in chapter 1 of [http://homepages.math.uic.edu/~marker/marker-thesis.pdf David Marker's thesis].
  
Title: Building Models of Strongly Minimal Theories - Part 1
+
=== January 25 - organizational meeting ===
  
Abstract: Since I'm talking in the Tuesday seminar as well, I'll use
+
We will meet to assign speakers to dates.
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 ===
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=== February 1 - Steffen Lempp ===
  
Title: Finding Definable Sets in Continuous Logic
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I will give an overview of the topics we will cover:  
  
Abstract: In order to be useful the notion of a 'definable set' in
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1. the base theory PA^- and the induction and bounding axioms for Sigma_n-formulas, and how they relate to each other,
continuous logic is stricter than a naive comparison to discrete logic
 
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 ===
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2. the equivalence of Sigma_n-induction with a version of Sigma_n-separation (proved by H. Friedman),
  
Title: Proper forcing
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3. the Grzegorczyk hierarchy of fast-growing functions,
  
Abstract: Although a given forcing notion may have nice properties on
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4. end extensions and cofinal extensions,
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 ===
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5. recursive saturation and resplendency,
  
Title: A survey of computable and constructive mathematics in economic history
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6. standard systems and coded types,
  
=== March 5, Tamvana Makulumi ===
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7. the McDowell-Specker Theorem that every model of PA has a proper elementary end extension, and
  
Title: Convexly Orderable Groups
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8. Gaifman's theorem that every model of PA has a minimal elementary end extension.
  
=== March 12, Dan Turetsky (University of Notre Dame) ===
+
I will sketch the basic definitions and state the main theorems, in a form that one can appreciate without too much
 +
background.
  
Title: Structural Jump
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=== February 8 - Karthik Ravishankar ===
  
=== March 19, Ethan McCarthy ===
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Title: Collection axioms
  
Title: Networks and degrees of points in non-second countable spaces
+
We will discuss parts 1 and 2 of Wong's notes.
  
=== April 2, Wil Cocke ===
+
== Previous Years ==
  
Title: Characterizing Finite Nilpotent Groups via Word Maps
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The schedule of talks from past semesters can be found [[Graduate Logic Seminar, previous semesters|here]].
 
 
Abstract: In this talk, we will examine a novel characterization of finite
 
nilpotent groups using the probability distributions induced by word
 
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 ===
 
 
 
Title: Quantum Randomness
 
 
 
Abstract: I will read the paper by Nies and Scholz where they define a notion of
 
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] ===
 
 
 
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, [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]].
 

Revision as of 19:06, 25 January 2022

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
  • Where: Van Vleck 901
  • Organizers: Jun Le Goh

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 2022

The graduate logic seminar this semester will be run as MATH 975. Please enroll if you wish to participate.

We plan to cover the first 9 parts of Tin Lok Wong's notes, as well as a few other relevant topics which are not covered in the notes:

  • Properness of the induction/bounding hierarchy (chapter 10 of Models of Peano Arithmetic by Kaye is a good source)
  • Tennenbaum's theorem (this is a quick consequence of the main theorem of part 4, so it should be combined with part 4 or part 5)
  • Other facts found in chapter 1 of David Marker's thesis.

January 25 - organizational meeting

We will meet to assign speakers to dates.

February 1 - Steffen Lempp

I will give an overview of the topics we will cover:

1. the base theory PA^- and the induction and bounding axioms for Sigma_n-formulas, and how they relate to each other,

2. the equivalence of Sigma_n-induction with a version of Sigma_n-separation (proved by H. Friedman),

3. the Grzegorczyk hierarchy of fast-growing functions,

4. end extensions and cofinal extensions,

5. recursive saturation and resplendency,

6. standard systems and coded types,

7. the McDowell-Specker Theorem that every model of PA has a proper elementary end extension, and

8. Gaifman's theorem that every model of PA has a minimal elementary end extension.

I will sketch the basic definitions and state the main theorems, in a form that one can appreciate without too much background.

February 8 - Karthik Ravishankar

Title: Collection axioms

We will discuss parts 1 and 2 of Wong's notes.

Previous Years

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