Graduate Logic Seminar: Difference between revisions

From UW-Math Wiki
Jump to navigation Jump to search
(21 intermediate revisions by 2 users not shown)
Line 9: Line 9:
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


== Fall 2021 tentative schedule ==
== Spring 2022 ==


To see what's happening in the Logic qual preparation sessions click [[Logic Qual Prep|here]].
The graduate logic seminar this semester will be run as MATH 975. Please enroll if you wish to participate.


=== September 14 - organizational meeting ===
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].


We met to discuss the schedule.
=== January 25 - organizational meeting ===


=== September 28 - Ouyang Xiating ===
We will meet to assign speakers to dates.


Title: First-order logic, database and consistent query answering
=== February 1 - Steffen Lempp ===


Abstract: Databases are a crucial component of many (if not all) modern
I will give an overview of the topics we will cover:  
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 ===
1. the base theory PA^- and the induction and bounding axioms for Sigma_n-formulas, and how they relate to each other,


Title: Notions of randomness for subsets of the Natural Numbers
2. the equivalence of Sigma_n-induction with a version of Sigma_n-separation (proved by H. Friedman),


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.
3. the Grzegorczyk hierarchy of fast-growing functions,


=== October 26 - Alice Vidrine ===
4. end extensions and cofinal extensions,


Title: Categorical logic for realizability, part III: Actual realizability
5. recursive saturation and resplendency,


Abstract: Realizability is an approach to semantics for non-classical logic that interprets propositions by sets of abstract computational data. In the present talk we describe the notion of a Schonfinkel algebra (also called a partial combinatory algebra), which gives us a very general notion of computation. We then describe the construction of a topos whose notions of morphism and subobject must respect the computational structure, and describe the unusual features of these toposes, closing with some discussion of Lawvere-Tierney topologies on such toposes.
6. standard systems and coded types,


(The abstracts for parts I and II, which were given in spring 2021, can be found [https://hilbert.math.wisc.edu/wiki/index.php/Graduate_Logic_Seminar,_previous_semesters#March_30_4PM_-_Alice_Vidrine here].)
7. the McDowell-Specker Theorem that every model of PA has a proper elementary end extension, and


=== November 9 - Antonio Nákid Cordero ===
8. Gaifman's theorem that every model of PA has a minimal elementary end extension.


=== November 23 - Antonio Nákid Cordero? ===
I will sketch the basic definitions and state the main theorems, in a form that one can appreciate without too much
background.


=== December 7 - John Spoerl ===
=== 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 ==
== 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 17:44, 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.