Upcoming Events

Logic Colloquium

March 24, 2017, 4:10 PM (60 Evans Hall)

Françoise Point
FNRS-FRS (UMons)

On expansions of (ℤ, +, 0)

In the special case of the structure (ℤ, +, 0), we will consider the following model-theoretic question: given a well-behaved first-order structure, which kind of predicates can one add and retain model-theoretic properties of the structure one started with, such as stability- like properties, quantifier elimination in a reasonable language, decidability. We will review recent results on stability properties of expansions of (ℤ, +, 0) by a unary predicate and we will make the comparison with former results on the decidability and model-completeness of the corresponding expansions of (ℤ, +, 0, <) (and if time permits, with the corresponding expansions of the field of real numbers).

Logic Colloquium

April 07, 2017, 4:10 PM (60 Evans Hall)

Pierre Simon
Assistant Professor of Mathematics, UC Berkeley

Title TBA

Alfred Tarski Lectures

April 10, 2017, 4:10 PM (50 Birge Hall)

Lou van den Dries
Professor, Department of Mathematics, University of Illinois at Urbana-Champaign

Model Theory as a Geography of Mathematics

I like to think of model theory as a geography of mathematics, especially of its “tame” side. Here tame roughly corresponds to geometric as opposed to combinatorial-arithmetic. In this connection I will discuss Tarski’s work on the real field, and the notion of o-minimality that it suggested.

A structure M carries its own mathematical territory with it, via interpretability: its own posets, groups, fields, and so on. Understanding this “world according to M” can be rewarding. Stability-like properties of M forbid certain combinatorial patterns, thus providing highly intrinsic and robust information about this world.

Alfred Tarski Lectures

April 12, 2017, 4:10 PM (50 Birge Hall)

Lou van den Dries
Professor, Department of Mathematics, University of Illinois at Urbana-Champaign

Orders of Infinity and Transseries

The “orders of Infinity” of the title are du Bois Reymond’s growth rates of functions, put on a firm basis by Hardy and Hausdorff. This led to the notion of a Hardy field (Bourbaki). Other ways of describing these orders of infinity are transseries (formal series containing powers of the variable x as well as exponential and logarithmic terms like ex and log x), and Conway’s surreal numbers. These topics are all closely related, with the differential field 𝕋 of transseries taking center stage.

Alfred Tarski Lectures

April 14, 2017, 4:10 PM (50 Birge Hall)

Lou van den Dries
Professor, Department of Mathematics, University of Illinois at Urbana-Champaign

Model Theory of Transseries: Results and Open Problems

The book Asymptotic Differential Algebra and Model Theory of Transseries (arXiv:1509.02588) by Aschenbrenner, van der Hoeven, and myself will soon appear as the Annals of Mathematics Studies, number 195. It contains the main results of twenty years of investigating 𝕋. One of these results is easy to state: The theory of this differential field is completely axiomatized by the requirements of being a Liouville closed H-field with small derivation and the intermediate value property for differential polynomials. I will explain the meaning of these terms, further results on 𝕋 and some consequences for what is definable in 𝕋.

I will also discuss some of the many attractive open problems in this area.

Logic Colloquium

April 21, 2017, 4:10 PM (60 Evans Hall)

Jana Marikova
Assistant Professor of Mathematics, Western Illinois University

Title TBA

May 05, 2017, 9:00 AM (McCone Hall, Room 141 from 9 AM to 2 PM; LeConte Hall, Room 3 from 2 PM to 5 PM)

Denis Hirschfeldt, Ehud Hrushovski, Michael Rathjen, John Steel

Logic at UC Berkeley

A two-day conference in mathematical logic and related areas organized by The Group in Logic and the Methodology of Science at UC Berkeley (logic.berkeley.edu). The conference is partly occasioned by the fact that the Group in Logic turns sixty next year.

In 1957, a group of faculty members, most of them from the departments of Mathematics and Philosophy, initiated a pioneering interdisciplinary graduate program leading to the degree of Ph.D. in Logic and the Methodology of Science. The Group has fostered interdisciplinary work in which logic has interacted with mathematics, philosophy, statistics, computer science, linguistics, physics and other disciplines.

While mathematical logic at UC Berkeley cannot be identified only with the Group in Logic, the Group has played a vital role in Berkeley’s worldwide prominence in mathematical logic and significantly contributed to making Berkeley a mecca since the fifties for people interested in mathematical logic and its applications. A full list of all those researchers in logic who taught at UC Berkeley, or studied at UC Berkeley, or visited Berkeley for shorter or longer periods would result in a who’s who of mathematical logic.

While marking an important moment for logic at UC Berkeley, the conference will be forward looking rather than merely celebratory. We have invited eight internationally prominent scholars to talk about the future of mathematical logic in their respective areas of specialization.

The first day of the conference will have four invited speakers in the so-called “foundational” areas: set theory, model theory, recursion theory, and proof theory. The second day will have four invited speakers in areas where mathematical logic plays a prominent role, namely philosophy of logic and mathematics, formal semantics for natural languages, modal logic, and foundations of computer science. The line up is given below.

May 5

set theory: John Steel (UC Berkeley), “Absolutely ordinal definable sets”

model theory: Ehud Hrushovski (Oxford University), “Reflections on model theory and foundations”

recursion theory: Denis Hirschfeldt (University of Chicago), “Computability Theory”

proof theory: Michael Rathjen (Leeds University), “On relating type theories to (intuitionistic) set theories”

May 6

philosophy of logic and mathematics: Jeremy Avigad (Carnegie Mellon University), “Modularity of Mathematics”

formal semantics for natural languages: Barbara Partee (University of Massachusetts at Amherst), “The Intertwining Influences of Logic, Philosophy, and Linguistics in the Development of Formal Semantics and Pragmatics”

modal logic: Johan van Benthem (University of Amsterdam, Stanford University, Tsinghua University), “Modal logic, on the cusp of philosophy and mathematics”

logic in computer science: Ronald Fagin (IBM Almaden Research Center), “Applying logic to practice in computer science”

May 06, 2017, 9:30 AM (Location TBA)

Jeremy Avigad, Johan van Benthem, Ronald Fagin, Barbara Partee

Logic at UC Berkeley

A two-day conference in mathematical logic and related areas organized by The Group in Logic and the Methodology of Science at UC Berkeley (logic.berkeley.edu). The conference is partly occasioned by the fact that the Group in Logic turns sixty next year.

In 1957, a group of faculty members, most of them from the departments of Mathematics and Philosophy, initiated a pioneering interdisciplinary graduate program leading to the degree of Ph.D. in Logic and the Methodology of Science. The Group has fostered interdisciplinary work in which logic has interacted with mathematics, philosophy, statistics, computer science, linguistics, physics and other disciplines.

While mathematical logic at UC Berkeley cannot be identified only with the Group in Logic, the Group has played a vital role in Berkeley’s worldwide prominence in mathematical logic and significantly contributed to making Berkeley a mecca since the fifties for people interested in mathematical logic and its applications. A full list of all those researchers in logic who taught at UC Berkeley, or studied at UC Berkeley, or visited Berkeley for shorter or longer periods would result in a who’s who of mathematical logic.

While marking an important moment for logic at UC Berkeley, the conference will be forward looking rather than merely celebratory. We have invited eight internationally prominent scholars to talk about the future of mathematical logic in their respective areas of specialization.

The first day of the conference will have four invited speakers in the so-called “foundational” areas: set theory, model theory, recursion theory, and proof theory. The second day will have four invited speakers in areas where mathematical logic plays a prominent role, namely philosophy of logic and mathematics, formal semantics for natural languages, modal logic, and foundations of computer science. The line up is given below.

May 5

set theory: John Steel (UC Berkeley), “Absolutely ordinal definable sets”

model theory: Ehud Hrushovski (Oxford University), “Reflections on model theory and foundations”

recursion theory: Denis Hirschfeldt (University of Chicago), “Computability Theory”

proof theory: Michael Rathjen (Leeds University), “On relating type theories to (intuitionistic) set theories”

May 6

philosophy of logic and mathematics: Jeremy Avigad (Carnegie Mellon University), “Modularity of Mathematics”

formal semantics for natural languages: Barbara Partee (University of Massachusetts at Amherst), “The Intertwining Influences of Logic, Philosophy, and Linguistics in the Development of Formal Semantics and Pragmatics”

modal logic: Johan van Benthem (University of Amsterdam, Stanford University, Tsinghua University), “Modal logic, on the cusp of philosophy and mathematics”

logic in computer science: Ronald Fagin (IBM Almaden Research Center), “Applying logic to practice in computer science”