# Difference between revisions of "Graduate Logic Seminar"

(75 intermediate revisions by 4 users not shown) | |||

Line 1: | Line 1: | ||

− | The Graduate Logic Seminar is an informal space where graduate | + | 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:''' | + | * '''When:''' Tuesdays 4-5 PM |

− | * '''Where:''' Van Vleck | + | * '''Where:''' Van Vleck 901 |

− | * '''Organizers:''' [https://www.math.wisc.edu/~ | + | * '''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. | ||

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 | ||

− | == Spring | + | == 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 [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]. | ||

− | + | === January 25 - organizational meeting === | |

− | + | We will meet to assign speakers to dates. | |

− | === February | + | === 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 == | |

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | ==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.