Welcome to New York Logic

Welcome to New York Logic!

Oct 30 Thursday Oct 31 Friday Nov 1 Saturday Nov 2 Sunday Nov 3 Monday Nov 4 Tuesday Nov 5 Wednesday

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Upcoming talks and events:

Model theory seminarFriday, October 31, 201410:45 amGC5382
Sebastien Vasey

Independence in tame abstract elementary classes

Carnegie Mellon University

Good frames are one of the main notions in Shelah’s classification theory for abstract elementary classes. Roughly speaking, a good frame describes a local forking-like notion for the class. In Shelah’s book, the theory of good frames is developed over hundreds of pages, and many results rely on GCH-like hypotheses and sophisticated combinatorial set theory.

In this talk, I will argue that dealing with good frames is much easier if one makes the global assumption of tameness (a locality condition introduced by Grossberg and VanDieren). I will outline a proof of the following result: Assume K is a tame abstract elementary class which has amalgamation, no maximal models, and is categorical in a cardinal of cofinality greater than the tameness cardinal. Then K is stable everywhere and has a good frame.

Set theory seminarFriday, October 31, 201412:00 pmGC 6417
Kameryn Williams

Scott’s problem for models of ZFC

The CUNY Graduate Center

Scott’s problem asks which Scott sets can be represented as standard systems of models of Peano arithmetic. Knight and Nadel proved in 1982 that every Scott set of cardinality $\le \omega_1$ is the standard system of some model of PA. Little progress has been made since then on the problem. I will present a modification of these results to models of ZFC and show that every Scott set of cardinality $\le \omega_1$ is the standard system of some model of ZFC. This talk will constitute the speaker’s oral exam.

Kolchin seminar in Differential AlgebraFriday, October 31, 201412:30 pmGC 5382
Anand Pillay

Interpretations and differential Galois extensions

Notre Dame University

We prove a number of results around finding strongly normal extensions of a differential field K, sometimes with prescribed properties, when the constants of K are not necessarily algebraically closed. The general yoga of interpretations and definable groupoids is used (in place of the Tannakian formalism in the linear case).

This is joint work with M. Kamensky.

Kolchin seminar in Differential AlgebraCUNY Logic WorkshopFriday, October 31, 20142:00 pmGC 6417
Anand Pillay

Mordell-Lang and Manin-Mumford in positive characteristic, revisited

Notre Dame University

We give a reduction of function field Mordell-Lang to function field Manin-Mumford, in positive characteristic. The upshot is another account of or proof of function field Mordell-Lang in positive characteristic, avoiding the recourse to difficult results on Zariski geometries.

(This work is joint with Benoist and Bouscaren.)

Logic, Probability and GamesFriday, October 31, 20144:00 pmRoom 2 (2nd floor) , Faculty House, Columbia University
Gregory Wheeler

The rise and fall of accuracy-first epistemology

Ludwig Maximilian University of Munich

Accuracy-first epistemology aims to supply non-pragmatic justifications for a variety of epistemic norms. The contemporary roots of accuracy-first epistemology are found in Jim Joyce’s program to reinterpret de Finetti’s scoring-rule arguments in terms of a “purely epistemic” notion of “gradational accuracy.” On Joyce’s account, scoring rules are conceived to measure the accuracy of an agent’s belief state with respect to the true state of the world, and Joyce argues that this notion of accuracy is a purely epistemic good. Joyce’s non-pragmatic vindication of probabilism, then, is an argument to the effect that a measure of gradational accuracy so imagined satisfies conditions that are close enough to those necessary to run a de Finetti style coherence argument. A number of philosophers, including Hannes Leitgeb and Richard Pettigrew, have joined Joyce’s program and gone whole hog. Leitgeb and Pettigrew, for instance, have argued that Joyce’s arguments are too lax and have put forward conditions that narrowing down the class of admissible gradational accuracy functions, while Pettigrew and his collaborators have extended the list of epistemic norms receiving an accuracy-first treatment, a program that he calls Evidential Decision Theory.

In this talk I report on joint work with Conor Mayo-Wilson that aims to challenge the core assumption of Evidential Decision Theory, which is the very idea of supplying a truly non-pragmatic justification for anything resembling the Von Neumann and Morgenstern axioms for a numerical epistemic utility function. Indeed, we argue that none of axioms have a satisfactory non-pragmatic justification, and we point to reasons why to suspect that not all the axioms could be given a satisfactory non-pragmatic justification. Our argument, if sound, has ramifications for recent discussions of “pragmatic encroachment”, too. For if pragmatic encroachment is a debate to do with whether there is a pragmatic component to the justification condition of knowledge, our arguments may be viewed to attack the true belief condition of (fallibilist) accounts of knowledge.

Model theory seminarFriday, November 7, 201410:45 amGC5382
David Marker

Representing Scott sets in algebraic settings

University of Illinois at Chicago

The longstanding problem of representing Scott sets as standard systems of models of Peano Arithmetic is one of the most vexing in the subject. We show that the analogous question has a positive solution for real closed fields and Presburger arithmetic. This is joint work with Alf Dolich, Julia Knight and Karen Lange.

Kolchin seminar in Differential AlgebraFriday, November 7, 201412:30 pmGC 5382
Michael Singer

The general solution of a first order differential polynomial

North Carolina State University

This is the title of a 1976 paper by Richard Cohn in which he gives a purely algebraic proof of a theorem (proved analytically by Ritt) that gives a bound on the number of derivatives needed to find a basis for the radical ideal of the general solution of such a polynomial. I will show that the method introduced by Cohn can be used to give a modern proof of a theorem of Hamburger stating that a singular solution of such a polynomial is either an envelope of a set of solutions or embedded in an analytic family of solutions depending on whether or not it corresponds to an essential singular component of this polynomial. I will also discuss the relation between this phenomenon and the Low Power Theorem. This will be an elementary talk with all these terms and concepts defined and explained.

CUNY Logic WorkshopFriday, November 7, 20142:00 pmGC 6417
Stevo Todorcevic

Choice principles and Ramsey theory

University of Toronto

This talk will provide an overview of results of Ramsey theory that have close relationships with constructions of models of ZF that distinguish between various forms of the Axiom of Choice. Some open problems and directions for further research will also be discussed.

NY Philosophical Logic GroupMonday, November 10, 20145:00 pmNYU Philosophy, 5 Washington Place, Room 302
Joel David Hamkins

Does definiteness-of-truth follow from definiteness-of-objects?

The City University of New York

This talk — a mix of mathematics and philosophy — concerns the extent to which we may infer definiteness of truth in a mathematical context from definiteness of the underlying objects and structure of that context. The philosophical analysis is based in part on the mathematical observation that the satisfaction relation for model-theoretic truth is less absolute than often supposed.  Specifically, two models of set theory can have the same natural numbers and the same structure of arithmetic in common, yet disagree about whether a particular arithmetic sentence is true in that structure. In other words, two models can have the same arithmetic objects and the same formulas and sentences in the language of arithmetic, yet disagree on their corresponding theories of truth for those objects. Similarly, two models of set theory can have the same natural numbers, the same arithmetic structure, and the same arithmetic truth, yet disagree on their truths-about-truth, and so on at any desired level of the iterated truth-predicate hierarchy.  These mathematical observations, for which I shall strive to give a very gentle proof in the talk (using only elementary classical methods), suggest that a philosophical commitment to the determinate nature of the theory of truth for a structure cannot be seen as a consequence solely of the determinateness of the structure in which that truth resides. The determinate nature of arithmetic truth, for example, is not a consequence of the determinate nature of the arithmetic structure N = {0,1,2,…} itself, but rather seems to be an additional higher-order commitment requiring its own analysis and justification.

This work is based on my recent paper, Satisfaction is not absolute, joint with Ruizhi Yang (Fudan University, Shanghai).

 

Model theory seminarFriday, November 14, 201410:45 amGC5382
Hunter Johnson

Some new maximum VC classes

John Jay College

Vapnik-Chervonenkis classes with the maximum property are in some sense the most perfect set systems of finite Vapnik-Chervonenkis dimension. Definability of maximum VC classes in model theoretic structures is closely tied to other measures of complexity such as dp-rank. In this talk we show that set systems realizable as sets of positivity for linear combinations of real analytic functions have the maximum property on sets in general position. This may have applications to proving lower bounds on dp-rank in certain theories.

Kolchin seminar in Differential AlgebraFriday, November 14, 201412:30 pmGC 5382
Rahim Moosa

Title TBA

University of Waterloo
CUNY Logic WorkshopFriday, November 14, 20142:00 pmGC 6417

Algebraic and model-theoretic methods in constraint satisfaction

Université Diderot – Paris 7

The Constraint Satisfaction Problem (CSP) of a first-order structure S in a finite relational language is the problem of deciding whether a given conjunction of atomic formulas in that language is satisfiable in S. Many classical computational problems can be modeled this way. The study of the complexity of CSPs involves an interesting combination of techniques from universal algebra, Ramsey theory, and model theory. I will present an overview over these techniques as well as some wild conjectures.

Model theory seminarFriday, November 21, 201410:45 am

Countable model theory and the complexity of isomorphism

University of Maryland

We discuss the Borel complexity of the isomorphism relation (for countable models of a first order theory) as the “right” generalization of the model counting problem. In this light we present recent results of Dave Sahota and the speaker which completely characterize the complexity of isomorphism for o-minimal theories, as well as recent work of Laskowski and Shelah which give a partial answer for omega-stable theories. Along the way, we introduce a few open problems and barriers to generalizing the existing results.

Model theory seminarFriday, December 5, 201410:45 am
Will Boney

TBA

University of Illinois Chicago
CUNY Logic WorkshopFriday, December 12, 20142:00 pmGC 6417
Andrew Brooke-Taylor

Title TBA

University of Bristol