Harvard Logic Colloquium

2018 Nov 28

Harvard Logic Colloquium: Charles Parsons "Kreisel and Gödel"

3:00pm to 4:00pm

Location: 

Logic Center, Room 420, 2 Arrow Street
We present a narrative of Georg Kreisel’s relation to Kurt Gödel, based on their correspondence. What appears to have been their first contact was Kreisel’s application in 1955 for a year’s membership at the Institute for Advanced Study. This was granted and extended for a second year. Then Kreisel returned to his position at the University of Reading in England. But he began a wandering life, spending time at Reading, Stanford University, the University of... Read more about Harvard Logic Colloquium: Charles Parsons "Kreisel and Gödel"
2018 Oct 24

Harvard Logic Colloquium: Sam Buss (UCSD) "Bounded Arithmetic, Expanders, and Monotone Propositional Proofs"

3:00pm to 4:00pm

Location: 

Logic Center, Room 420, 2 Arrow Street
This talk discusses a new combinatorial proof of the existence of expander graphs, which can be carried out in the bounded arithmetic theory VNC1 corresponding to alternating linear time. As an application, we prove that the monotone propositional sequent calculus polynomially simulates the full propositional sequent calculus. Prior to this, only a quasipolynomial simulation was known. Joint work with Valentine Kabanets, Antonina Kolokolova, and Michal Koucky.
2018 Apr 12

Harvard Logic Colloquium: Boris Zilber (Oxford)

4:00pm

Location: 

Logic Center, Room 420, 2 Arrow Street

Boris Zilber (Oxford): Between Model Theory and Physics

There are several important issues in physics which model theory have potential to help with. First of all, there is the issue of adequate language and formalism, and closely related to this there is a more specific problem of giving rigorous meanings to limits and integrals used by physicists. I will present a variation of ‘positive model theory’ which addresses these issues and discuss some progress in defining...

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2018 Mar 22

Harvard Logic Colloquium: Donald Martin (UCLA)

4:00pm to 5:00pm

Location: 

Logic Center, Room 420, 2 Arrow Street

Donald Martin (UCLA): Cantor's Grundlagen

Cantor’s early (1883) Grundlagen einer allgemeinen Mannigfaltigkeitslehre is badly organized and has
important errors and omissions. Nevertheless it is rich in content, and its concepts are in some ways
superior to Cantor’s later ones.

I will mainly concentrate on a few aspects of Grundlagen: (1) what might be called Cantor’s quasiaxiomatic,
iterative account of ordinal numbers; (2) the role that something like a Replacement Axiom
plays in this account; (3) the...

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2016 Nov 03

Harvard Logic Colloquium: Theodore Slaman

4:00pm to 6:00pm

Location: 

Logic Center, Room 420, 2 Arrow Street

Theodore A. Slaman (University of California Berkeley): Recursion Theory and Diophantine Approximation

Recursion Theory deals with the definability of sets, especially sets of natural numbers or equivalently
real numbers. Diophantine Approximation deals with the approximation of real numbers by rational
numbers, which can be viewed as a number theoretic form of definability. We will discuss connections
between these areas.

2016 Oct 20

Harvard Logic Colloquium: Joel Hamkins

4:00pm to 5:00pm

Location: 

Logic Center, Room 420, 2 Arrow Street

Joel Hamkins (City University of New York): Recent Advances in Set-theoretic Geology

Set-theoretic geology is the study of the set-theoretic universe V in the context of all its ground models and those of its forcing extensions. For example, a bedrock of the universe is a minimal ground model of it and the mantle is the intersection of all grounds. In this talk, I shall explain some recent advances, including especially the breakthrough result of Toshimichi Usuba, who proved the strong downward directed grounds hypothesis: for any set-indexed family of...

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2015 Feb 23

Harvard Logic Seminar

4:30pm to 5:30pm

Location: 

Logic Center, Room 420, 2 Arrow Street

Will Boney (University of Illinois at Chicago) "Tameness in Abstract Elementary Classes"

Tameness is a locality property of Galois types in AECs. Since its isolation by Grossberg and VanDieren 10 years ago, it has been used to prove new results (upward categoricity transfer, stability transfer) and replace set theoretic hypotheses (existence of independence notions). In this talk, we will outline the basic definitions, summarize some key results, and discuss some open questions related to tameness.

2014 Nov 19

Harvard Logic Colloquium

4:30pm to 5:30pm

Location: 

Logic Center, Room 420, 2 Arrow Street

Maryanthe Malliaris (University of Chicago) "Comparing the complexity of unstable theories"

In 1967 Keisler posed the problem of Keisler’s order, a suggested program for comparing the complexity of classes of mathematical structures using an asymptotic (ultrapower) point of view. The talk will be about recent results in this area, due to Malliaris and to Malliaris and Shelah, which advance this program by developing a sort of fine structure theory for pseudofinite behavior in model theory. In particular, the focus will be on simple theories, a key model-theoretic...

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2014 Oct 29

Harvard Logic Colloquium

4:30pm to 5:30pm

Location: 

Logic Center, Room 408, 2 Arrow Street

Joan Bagaria (Universitat de Barcelona) "Reflection phenomena in the set-theoretic universe"

The phenomenon of reflection occurs at different layers of the set-theoretic universe V, and strengthened forms of reflection associated to each layer give rise to natural additional axioms for set theory of different sorts. In this talk we shall review some strong forms of reflection pertaining to different layers such as the class of ordinals, some inner models, V itself, and even the ideal extensions of V provided by the forcing method, while exposing some intriguing...

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2014 Sep 24

Harvard Logic Seminar

4:30pm to 5:30pm

Location: 

Logic Center, Room 408, 2 Arrow Street

Gil Sagi (Ludwig-Maximilians-Universität München) "What is a Fixed Term?"

In standard model-theoretic semantics, logical terms are said to be fixed in the system while nonlogical terms remain variable. Much effort has been devoted to characterizing logical terms, those terms that should be fixed, but little has been said on their role in logical systems: on what fixing them precisely amounts to. My proposal is that when a term is considered logical in a system, what gets fixed is its intension rather than its extension. I provide a rigorous way of spelling out this idea. Further, I...

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