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 a space focused principally on practicing presentation skills or learning materials that are not usually presented in 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 4p-5p
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* '''When:''' Tuesdays 4-5 PM
* '''Where:''' Van Vleck B223.
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* '''Where:''' Van Vleck 901
* '''Organizers:''' [https://www.math.wisc.edu/~omer/ Omer Mermelstein]
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* '''Organizers:''' [https://www.math.wisc.edu/~jgoh/ 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.
 
The talk schedule is arranged at the beginning of each semester. If you would like to participate, please contact one of the organizers.
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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:  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.
  
== Fall 2019 - Tentative schedule ==
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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].
  
=== September 5 - Organizational meeting ===
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=== January 25 - organizational meeting ===
  
=== September 9 - No seminar ===
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We will meet to assign speakers to dates.
  
=== September 16 - Daniel Belin ===
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=== February 1 - Steffen Lempp ===
Title: Lattice Embeddings of the m-Degrees and Second Order Arithmetic
 
  
Abstract: Lachlan, in a result later refined and clarified by Odifreddi, proved in 1970 that initial segments of the m-degrees can be embedded as an upper semilattice formed as the limit of finite distributive lattices. This allows us to show that the many-one degrees codes satisfiability in second-order arithmetic, due to a later result of Nerode and Shore. We will take a journey through Lachlan's rather complicated construction which sheds a great deal of light on the order-theoretic properties of many-one reducibility.
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I will give an overview of the topics we will cover:
  
=== September 23 - Daniel Belin ===
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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,
  
Title: Lattice Embeddings of the m-Degrees and Second Order Arithmetic - Continued
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2. the equivalence of Sigma_n-induction with a version of Sigma_n-separation (proved by H. Friedman),
  
=== September 30 - Josiah Jacobsen-Grocott ===
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3. the Grzegorczyk hierarchy of fast-growing functions,
  
Title: Scott Rank of Computable Models
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4. end extensions and cofinal extensions,
  
Abstract: Infinatary logic extends the notions of first order logic by allowing infinite formulas. Scott's Isomorphism Theorem states that any countable structure can be characterized up to isomorphism by a single countable sentence. Closely related to the complexity of this sentence is what is known as the Scott Rank of the structure. In this talk we restrict our attention to computable models and look at an upper bound on the Scott Rank of such structures.
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5. recursive saturation and resplendency,
  
=== October 7 - Josiah Jacobsen-Grocott ===
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6. standard systems and coded types,
  
Title: Scott Rank of Computable Codels - Continued
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7. the McDowell-Specker Theorem that every model of PA has a proper elementary end extension, and
  
=== October 14 - Tejas Bhojraj ===
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8. Gaifman's theorem that every model of PA has a minimal elementary end extension.
  
Title: Solovay and Schnorr randomness for infinite sequences of qubits.
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I will sketch the basic definitions and state the main theorems, in a form that one can appreciate without too much
 +
background.
  
Abstract : We define Solovay and Schnorr randomness in the quantum setting. We then prove quantum versions of the law of large numbers and of the Shannon McMillan Breiman theorem (only for the iid case) for quantum Schnorr randoms.
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=== February 8 - Karthik Ravishankar ===
  
=== October 21 - Tejas Bhojraj ===
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Title: Collection axioms
  
Title: Solovay and Schnorr randomness for infinite sequences of qubits.
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We will discuss parts 1 and 2 of Wong's notes.
  
=== October 28 - Two short talks ===
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=== February 15 - Karthik Ravishankar, Yunting Zhang ===
  
'''Iván Ongay Valverde''' - Exploring different versions of the Semi-Open Coloring Axiom (SOCA)
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Title: Collection axioms/The Weak König Lemma
  
In 1985, Avraham, Rubin and Shelah published an article where they introduced different coloring axioms. The weakest of them, the Semi-Open Coloring Axiom (SOCA), states that given an uncountable second countable metric space, $E$, and $W\subseteq E^{\dagger}:=E\times E\setminus \{(x, x) :x \in E\}$ open and symmetric, there is an uncountable subset $H\subseteq E$ such that either $H^{\dagger}\subseteq W$ or $H^{\dagger}\cap W=\emptyset$. We say that $W$ is an open coloring and $H$ is a homogeneous subset of $E$. This statement contradicts CH but, as shown also by Avraham, Rubin and Shelah, it is compatible with the continuum taking any other size. This classic paper leaves some questions open (either in an implicit or an explicit way):
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Karthik will finish part 2 of Wong's notes. Then Yunting will start on part 3 of Wong's notes.
  
- Is the axiom weaker if we demand that $W$ is clopen?
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=== February 22 - Yunting Zhang ===
- If the continuum is bigger than $\aleph_2$, can we ask that $H$ has the same size as $E$?
 
- Can we expand this axiom to spaces that are not second countable and metric?
 
  
These questions lead to different versions of SOCA. In this talk, we will analyze how they relate to the original axiom.
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Title: The Weak König Lemma
  
'''James Earnest Hanson'''
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We will finish part 3 of Wong's notes.
  
TBA
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=== March 22 - Ang Li ===
  
=== November 4 - Two short talks ===
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Title: The Arithmetized Completeness Theorem
  
Manlio Valenti and Patrick Nicodemus
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We will discuss part 4 of Wong's notes.
  
=== November 11 - Manlio Valenti I ===
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=== March 29 - Ang Li ===
  
=== November 18 - Manlio Valenti II ===
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Title: The Arithmetized Completeness Theorem
  
=== November 25 - Two short talks ===
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We will finish part 4 of Wong's notes.
Speakers TBD
 
  
=== December 2 - Iván Ongay Valverde I ===
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=== April 5 - Antonio Nákid Cordero ===
  
=== December 9 - Iván Ongay Valverde II ===
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Title: Semiregular cuts
  
==Previous Years==
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We will start on part 5 of Wong's notes.
 +
 
 +
=== April 12 - Antonio Nákid Cordero/Alice Vidrine ===
 +
 
 +
Title: Semiregular cuts/End and cofinal extensions
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 +
We will finish part 5 of Wong's notes and then start on part 6.
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 +
=== April 19 - Alice Vidrine ===
 +
 
 +
Title: End and cofinal extensions
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 +
We will finish part 6 of Wong's notes.
 +
 
 +
=== May 3 - No seminar today ===
 +
 
 +
== 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]].

Revision as of 12:44, 2 May 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.

February 15 - Karthik Ravishankar, Yunting Zhang

Title: Collection axioms/The Weak König Lemma

Karthik will finish part 2 of Wong's notes. Then Yunting will start on part 3 of Wong's notes.

February 22 - Yunting Zhang

Title: The Weak König Lemma

We will finish part 3 of Wong's notes.

March 22 - Ang Li

Title: The Arithmetized Completeness Theorem

We will discuss part 4 of Wong's notes.

March 29 - Ang Li

Title: The Arithmetized Completeness Theorem

We will finish part 4 of Wong's notes.

April 5 - Antonio Nákid Cordero

Title: Semiregular cuts

We will start on part 5 of Wong's notes.

April 12 - Antonio Nákid Cordero/Alice Vidrine

Title: Semiregular cuts/End and cofinal extensions

We will finish part 5 of Wong's notes and then start on part 6.

April 19 - Alice Vidrine

Title: End and cofinal extensions

We will finish part 6 of Wong's notes.

May 3 - No seminar today

Previous Years

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