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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.  +  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 4p5p  +  * '''When:''' TBA 
−  * '''Where:''' Van Vleck B223.  +  * '''Where:''' on line (ask for code). 
−  * '''Organizers:''' [https://www.math.wisc.edu/~omer/ Omer Mermelstein]  +  * '''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: joingradlogicsem@lists.wisc.edu   Sign up for the graduate logic seminar mailing list: joingradlogicsem@lists.wisc.edu 
   
 +  == Spring 2021  Tentative schedule == 
   
−   +  Email Jun Le if you would like to speak! 
−  == Fall 2019  Tentative schedule ==
 
−   
−  === September 5  Organizational meeting ===
 
−   
−  === September 9  No seminar ===
 
−   
−  === September 16  Daniel Belin ===
 
−  Title: Lattice Embeddings of the mDegrees and Second Order Arithmetic
 
−   
−  Abstract: Lachlan, in a result later refined and clarified by Odifreddi, proved in 1970 that initial segments of the mdegrees can be embedded as an upper semilattice formed as the limit of finite distributive lattices. This allows us to show that the manyone degrees codes satisfiability in secondorder 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 ordertheoretic properties of manyone reducibility.
 
−   
−  === September 23  Daniel Belin ===
 
−   
−  Title: Lattice Embeddings of the mDegrees and Second Order Arithmetic  Continued
 
−   
−  === September 30  Josiah JacobsenGrocott ===
 
−   
−  Title: Scott Rank of Computable Models
 
−   
−  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.
 
−   
−  === October 7  Josiah JacobsenGrocott ===
 
−   
−  Title: Scott Rank of Computable Codels  Continued
 
−   
−  === October 14  Tejas Bhojraj ===
 
−   
−  Title: Solovay and Schnorr randomness for infinite sequences of qubits.
 
−   
−  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.
 
−   
−  === October 21  Tejas Bhojraj ===
 
−   
−  Title: Solovay and Schnorr randomness for infinite sequences of qubits.
 
−   
−  === October 28  Two short talks ===
 
−   
−  '''Iván Ongay Valverde'''  Exploring different versions of the SemiOpen Coloring Axiom (SOCA)
 
−   
−  In 1985, Avraham, Rubin and Shelah published an article where they introduced different coloring axioms. The weakest of them, the SemiOpen 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):
 
−   
−   Is the axiom weaker if we demand that $W$ is clopen?
 
−   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.
 
−   
−  '''James Earnest Hanson'''
 
−   
−  TBA
 
−   
−  === November 4  Two short talks ===
 
−   
−  Manlio Valenti and Patrick Nicodemus
 
−   
−  === November 11  Manlio Valenti I ===
 
−   
−  === November 18  Manlio Valenti II ===
 
−   
−  === November 25  Two short talks ===
 
−  Speakers TBD
 
−   
−  === December 2  Iván Ongay Valverde I ===
 
−   
−  === December 9  Iván Ongay Valverde II ===
 
   
 ==Previous Years==   ==Previous Years== 
   
 The schedule of talks from past semesters can be found [[Graduate Logic Seminar, previous semestershere]].   The schedule of talks from past semesters can be found [[Graduate Logic Seminar, previous semestershere]]. 