Graduate Logic Seminar: Difference between revisions

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== Fall 2024 ==
== Fall 2024 ==


The seminar will be run as a 1-credit seminar Math 975 . In Fall 2024, the topic will be Higher Computability Theory. If you are not enrolled but would like to audit it, please contact [mailto:soskova@wisc.edu Mariya Soskova].
The seminar will be run as a 1-credit seminar Math 975 . In Fall 2024, the topic will be Higher Computability Theory. We will follow notes by Noam Greenberg. If you are not enrolled but would like to audit it, please contact [mailto:soskova@wisc.edu Mariya Soskova].


Presentation Schedule: https://docs.google.com/spreadsheets/d/1ect-dgHdoHOgq4-5BGFiDh6pPThLfDg69Yg__-b_5RY/edit?usp=sharing
Presentation Schedule: [https://docs.google.com/spreadsheets/d/1ect-dgHdoHOgq4-5BGFiDh6pPThLfDg69Yg__-b_5RY/edit?usp=sharing Sign up here.]


Zoom link for remote attendance: https://uwmadison.zoom.us/j/96168027763?pwd=bGdvL3lpOGl6QndQcG5RTFUzY3JXQT09 (Meeting ID: 961 6802 7763, Password: 975f23)
Notes: [https://uwmadison.box.com/s/j3xftdj1i70d4lblxhzswhg9e25ajcpq Download the notes here.] You will need your UW-login. Please, do not distribute these notes without permission from the author.
 
<!--Zoom link for remote attendance: https://uwmadison.zoom.us/j/96168027763?pwd=bGdvL3lpOGl6QndQcG5RTFUzY3JXQT09 (Meeting ID: 961 6802 7763, Password: 975f23)-->


=== '''September 9 - Organizational Meeting''' ===
=== '''September 9 - Organizational Meeting''' ===


Mariya Soskova will start with the first to sections from the notes.
Mariya Soskova will start with the first sections from the notes.


We will then assign speakers to dates and topics.
We will then assign speakers to dates and topics.


=== '''February 5 - Taeyoung Em''' ===
=== '''September 16 - Sections 1.2-1.4''' ===
'''Title:''' Introduction to forcing
 
'''Abstract:''' We introduce new definitions and properties regarding forcing.
 
=== '''February 12 - Hongyu Zhu''' ===
'''Title:''' Slaman-Woodin Forcing and the Theory of Turing Degrees
 
'''Abstract:''' We will discuss how to use Slaman-Woodin forcing to interpret true second(first, resp.)-order arithmetic in the Turing degrees (Turing degrees below 0', resp.), thereby showing they have the same Turing degree.
 
=== '''February 19 - John Spoerl''' ===
'''Title:''' Forcing with Trees - Spector's and Sack's Minimal Degrees


'''Abstract:''' We'll take a look at Spector's forcing which uses perfect trees as conditions. Then we'll see where we might make some improvements which leads to Sack's sharpening of Spector's theorem: there is a minimal degree below 0'.  
Kanav Madhura will continue with Sections 1.2-1.4.  


=== '''February 26 - Karthik Ravishankar''' ===
=== '''September 23 - Sections 1.3-1.4 and 2.1-2.2''' ===
'''Title:''' The 3 element chain as an initial segment of the Turing Degrees


'''Abstract:''' In this talk, we'll look at the construction of a minimal degree with a strong minimal cover which shows that the three-element chain can be embedded as an initial segment of the Turing Degrees. The construction builds off ideas of Spector's minimal degree with stronger assumptions on the forcing conditions used. If time permits, we'll also talk about Copper's Jump Inversion building off Sack's construction.
Kanav Madhura will continue with Sections 1.3-1.4. Lucas Duckworth will be ready with Sections 2.1 and 2.2 should there be time.  


=== '''March 4 - Karthik Ravishankar''' ===
=== '''September 30 - Sections 2.2 and 2.3-2.5''' ===
'''Title:''' Bushy Tree forcing and constructing a minimal degree which is DNC


'''Abstract:''' We shall look at a forcing technique called Bushy Tree forcing using it to show that there is no uniform way to compute a DNC_2 from a DNC_3 function and that there is a DNC function that is weak in the sense that it does not compute a computably bounded DNC function. We present a few other results along these lines and sketch the construction of a minimal degree that is DNC relative to any given oracle using bushy tree forcing.
Lucas Duckworth will finish Section 2.2. Karthik Ravishankar will begin 2.3, 2.4, and 2.5.
=== '''October 7th -  Sections 2.4 and 2.5''' ===


=== '''March 11 - Josiah Jacobsen-Grocott''' ===
Karthik Ravishankar will  finish, 2.4, and 2.5.  Liang Yu will give a talk at 4:00pm.
'''Title:''' A uniformly e-pointed tree on Baire space without dead ends that is not of cototal degree


'''Abstract:''' A set is cototal if it is enumeration reducible to its complement. A tree is e-point if every path on the tree can enumerate the tree. McCathy proved that these notions are equivalent up to e-degree when considering e-pointed trees on cantor space. This fails when considering trees on Baire space. We give an example of a simple forcing construction that produces e-pointed trees on Baire space. We carefully analyze this forcing partial order to prove that generic e-pointed trees without dead ends are not of cototal degree.
=== '''October 14th -  Sections 2.6 and 2.7''' ===


=== '''March 18 - Alice Vidrine''' ===
Bjarki Gunnarsson  will present Sections 2.6 and 2.7
'''Title:''' There is no non-computable bi-introreducible set


'''Abstract:''' A set is said to be bi-introreducible if it can be computed by any of its infinite subsets, or any infinite subset of its complement. This talk will detail a Matthias forcing construction used to prove a theorem by Seetapun which implies that the bi-introreducible sets are exactly the computable sets.
=== '''October 21th -  Section 3.1''' ===


=== '''April 1 - Hongyu Zhu''' ===
Karthik Ravishankar will present Section 3.1
'''Title:''' The Conservativeness of WKL_0 over RCA_0 for <math>\Pi_1^1</math>-formulas


'''Abstract:''' We will see how to use forcing to construct models of WKL_0 from models of RCA_0 while preserving certain arithmetical truths, thereby showing that WKL_0 is <math>\Pi_1^1</math>-conservative over RCA_0.
=== '''October 28th -  Sections 3.2 and 3.3''' ===


=== '''April 8 - Cancelled''' ===
Karthik Ravishankar will finish Sections 3.2  and John Spoerl will begin Section 3.3


=== '''April 15 - Ang Li''' ===
=== '''November 4th - Sections 3.3 and 3.4''' ===
'''Title:''' Steel Forcing without Generalized Ramified Forcing Language


'''Abstract:''' In this talk, we will introduce Steel forcing, also known as "forcing with tagged trees",  using a restricted infinitary language. We will prove the retagging lemma and show the example that Well-Foundededness and Unique Branch are not Borel separable. If time permits, we will talk about another example in descriptive set theory that uses steel forcing purely topologically.
John Spoerl will finish Sections 3.3 and 3.4


=== '''April 22 - Antonio Nakid Cordero''' ===
=== '''November 11th - Section 4.1''' ===
'''Title:''' Kumabe-Slaman Forcing and Definability of the Turing Jump


'''Abstract:''' Slaman and Woodin's Analysis of the automorphisms of the Turing Degrees gave as a consequence the definability of the double jump. We will prove a Posner-Robinson type theorem for n-CEA operators by Kumabe-Slaman forcing that, together with the definability of the double jump, gives the definability of the single jump.
Antonion Nakid-Cordero will present Section 4.1


=== '''April 29 - John Spoerl''' ===
=== '''November 19th - Sections 4.1 and 4.2''' ===
'''Title:''' Forcing in Set Theory


'''Abstract:''' Despite the theme of this seminar being about computability-theoretic forcing, the forcing method is most famously used in set theory to prove various consistency results. The most important use of forcing was its invention by Paul Cohen to show the independence of the continuum hypothesis and the axiom of choice from ZFC. I'll discuss the subtleties and development of forcing in set theory and sketch the method by which one can build and control new models of ZF(C).
Start 4:00PM in VV901! Antonion Nakid-Cordero will continue with Section 4.1, Ang Li will begin Section 4.2.


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Revision as of 19:37, 18 November 2024

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 3:30-4:30 PM
  • Where: Van Vleck B123
  • Organizer: Mariya Soskova

The talk schedule is arranged at the beginning of each semester. If you would like to participate, please contact the organizers.

Sign up for the graduate logic seminar mailing list: join-grad-logic-sem@lists.wisc.edu

Fall 2024

The seminar will be run as a 1-credit seminar Math 975 . In Fall 2024, the topic will be Higher Computability Theory. We will follow notes by Noam Greenberg. If you are not enrolled but would like to audit it, please contact Mariya Soskova.

Presentation Schedule: Sign up here.

Notes: Download the notes here. You will need your UW-login. Please, do not distribute these notes without permission from the author.


September 9 - Organizational Meeting

Mariya Soskova will start with the first sections from the notes.

We will then assign speakers to dates and topics.

September 16 - Sections 1.2-1.4

Kanav Madhura will continue with Sections 1.2-1.4.

September 23 - Sections 1.3-1.4 and 2.1-2.2

Kanav Madhura will continue with Sections 1.3-1.4. Lucas Duckworth will be ready with Sections 2.1 and 2.2 should there be time.

September 30 - Sections 2.2 and 2.3-2.5

Lucas Duckworth will finish Section 2.2. Karthik Ravishankar will begin 2.3, 2.4, and 2.5.

October 7th - Sections 2.4 and 2.5

Karthik Ravishankar will finish, 2.4, and 2.5. Liang Yu will give a talk at 4:00pm.

October 14th - Sections 2.6 and 2.7

Bjarki Gunnarsson will present Sections 2.6 and 2.7

October 21th - Section 3.1

Karthik Ravishankar will present Section 3.1

October 28th - Sections 3.2 and 3.3

Karthik Ravishankar will finish Sections 3.2 and John Spoerl will begin Section 3.3

November 4th - Sections 3.3 and 3.4

John Spoerl will finish Sections 3.3 and 3.4

November 11th - Section 4.1

Antonion Nakid-Cordero will present Section 4.1

November 19th - Sections 4.1 and 4.2

Start 4:00PM in VV901! Antonion Nakid-Cordero will continue with Section 4.1, Ang Li will begin Section 4.2.


Previous Years

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

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