# Difference between revisions of "Graduate Logic Seminar"

Line 25: | Line 25: | ||

I will give an overview of the topics we will cover: | 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 | + | 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) | + | |

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

4. end extensions and cofinal extensions, | 4. end extensions and cofinal extensions, |

## Revision as of 16:27, 18 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. Giafman'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.

## Previous Years

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