Welcome to New York Logic!

May 4 Wednesday | May 5 Thursday | May 6 Friday | May 7 Saturday | May 8 Sunday | May 9 Monday | May 10 Tuesday |
---|---|---|---|---|---|---|

**→** go to the Calendar

## Upcoming talks and events:

# Stochastic – calculus

It is shown how the operators in the “graph model” for calculus (which can function as a programming language for Recursive Function Theory) can be expanded to allow for “random combinators.” The result then is a semantics for a new language for random algorithms. The author wants to make a plea for finding applications.

This talk is part of the Computer Science Colloquium at the CUNY Graduate Center.

# A position in infinite chess with game value $\omega^4$

This talk is a more detailed version of the presentation that I gave on set theory day.

I present a position in infinite chess with game value $\omega^4$. Informally speaking, this means that one side can force a win in $\omega^4$ many moves, or that the game is equivalent to the game of counting down from $\omega^4$. This result, joint with Hamkins and Evans, improved on the previous best result of $\omega^3$.

# Imaginaries in valued fields of positive characteristic

I will discuss the basic properties of the theory SCVF of separably closed valued fields, and the closely related theory SCVH of separably closed valued fields equipped with Hasse derivations. The main new result is elimination of imaginaries (in a suitable language). This is joint work with Martin Hils and Silvain Rideau.

# Edmund Husserl’s Philosophy of Arithmetic

Edmund Husserl, the principal founder of phenomenology, is well known for his contributions to philosophy. What is less known is his early work in mathematics. Husserl studied under Kronceker and Weierstrass in Berlin, and got his Ph.D. in 1883 in Vienna working on the calculus of variations under supervision of Leo Königsberger. Under influence of Franz Brentano, he moved to philosophy, and in from 1901 to 1916 he taught philosophy in Göttingen, where he interacted with Hilbert. In “Logic and Philosophy of Mathematics in the Early Husserl” Springer 2010, Stefania Centrone analyses Husserl’s work on foundations of mathematics from that period, and shows its connections to Hilbert’s ideas. I will say a few words about phenomenology, and I’ll talk about fragments of Husserl’s “Philosophy of Arithmetic.”

# The Dixmier-Moeglin problem for D-varieties

By a D-variety we mean, following Buium, an algebraic variety V over an algebraically closed field k equipped with a regular section s: V–> TV to the tangent bundle of V. (This is equivalent to the category of finite dimensional differential-algebraic varieties over the constants.) There are natural notions of D-rational map and D-subvariety. Motivated by problems in noncommutative algebra we are lead to ask under what conditions (V,s) has a maximum proper D-subvariety over k. (Model-theoretically this asks when the generic type is isolated.) A necessary condition is that (V,s) does not admit a nonconstant D-constant, that is, a D-rational map from (V,s) to the affine line equipped with the

zero section. When is this condition sufficient? I will discuss this rather open-ended problem, including some known cases.

# Trichotomy principle for partial differential fields

The Zilber trichotomy principle gives a precise sense in which the structure on a sufficiently well behaved one-dimensional set must have one of only three possible kinds: disintegrated (meaning that there may be some isolated correspondences, but nothing else), linear (basically coming from an abelian group with no extra structure), or algebro-geometric (essentially coming from an algebraically closed field). This principle is true in differentially closed fields when “one dimensional” is understood as “strongly minimal” (proven by Hrushovski and Sokolovic using the theory of Zariski geometries and then by Pillay and Ziegler using jet spaces).

When working with differentially closed fields with finitely many, but more than one, distinguished commuting derivations, there are sets which from a certain model theoretic point of view (having to do with the notion of a regular type) are one dimensional even though they are infinite dimensional from the point of view of differential dimension. Moosa, Pillay and Scanlon showed that a weakening of the trichotomy principle is true for these sets: if there is a counter example to the trichotomy principle, then one can be found for a set defined by linear PDEs.

In this lecture, I will explain in detail what the trichotomy principle means in differential algebra, how the reduction to the linear case works, and then how one might approach the open problems.

This is a joint event of the CUNY Logic Workshop and the Kolchin Seminar in Differential Algebra, as part of a KSDA weekend workshop.

# $\omega$-stability and Morley rank of bilinear maps, rings and nilpotent groups

In this talk I will present our recent results on the algebraic structure of $\omega$-stable bilinear maps, arbitrary rings and nilpotent groups. I will also discuss some rather complete structure theorems for the above structures in the finite Morley rank case. The main technique in this work is associating a canonical scalar (commutative associative unitary) ring to a bilinear map. This canonical scalar ring happens to preserve many of the logical and algebraic properties of the bilinear map. This talk is based on the joint work with Alexei Miasnikov.