# Past Logic Seminar

14 June 2012
17:00
Özlem Beyarslan (Bogazici)
Abstract
A pseudofinite field is a perfect pseudo-algebraically closed (PAC) field which has $\hat{\mathbb{Z}}$ as absolute Galois group. Pseudofinite fields exists and they can be realised as ultraproducts of finite fields. A group $G$ is geometrically represented in a theory $T$ if there are modles $M_0\prec M$ of $T$, substructures $A,B$ of $M$, $B\subset acl(A)$, such that $M_0\le A\le B\le M$ and $Aut(B/A)$ is isomorphic to $G$. Let $T$ be a complete theory of pseudofinite fields. We show that, geometric representation of a group whose order is divisibly by $p$ in $T$ heavily depends on the presence of $p^n$'th roots of unity in models of $T$. As a consequence of this, we show that, for almost all completions of the theory of pseudofinite fields, over a substructure $A$, algebraic closure agrees with definable closure, if $A$ contains the relative algebraic closure of the prime field. This is joint work with Ehud Hrushovski.
• Logic Seminar
24 May 2012
17:00
Pierre Simon (Ecole Normale Superiore)
Abstract
I will explain how to define a notion of stable-independence in NIP theories, which is an attempt to capture the "stable part" of types.
• Logic Seminar
17 May 2012
17:00
*Cancelled*
Abstract
• Logic Seminar
10 May 2012
17:00
Jamshid Derakhshan
Abstract
This is joint work with Raf Cluckers, Eva Leenknegt, and Angus Macintyre.<br /><br />We give a first-order definition, in the ring language, of the ring of p-adic integers inside the field&nbsp;p-adic numbers which works uniformly for all p and for valuation rings of all finite field extensions and of&nbsp;all local&nbsp;fields of positive characteristic p, and in many other Henselian valued fields as well. The formula canbe taken existential-universal in the ring language. Furthermore, we show the negative result that in the language&nbsp;of rings there does not exist a uniform definition by an existential formula and neither by a universal formula. For any fixed general p-adic field we give an existential formula in the ring language which defines the valuation ring.</p> <p>We also state some connections to some open problems.</p>
• Logic Seminar
26 April 2012
17:00
Angus Macintyre (QMUL)
Abstract
Shapiro's Conjecture says that two classical exponential polynomials over the complexes can have infinitely many common zeros only for algebraic reasons. I will explain the history of this, the connection to Schanuel's Conjecture, and sketch a proof for the complexes using Schanuel, as well as an unconditional proof for Zilber's fields.
• Logic Seminar
8 March 2012
17:00
Abstract
• Logic Seminar
1 March 2012
17:00
Dugald Macpherson (Leeds)
Abstract
I will give an overview of the description of imaginaries in algebraically closed (and some other) valued fields, and then discuss the related issue for valued fields with analytic structure (in the sense of Lipshitz-Robinson, and Denef – van Den Dries). In particular, I will describe joint work with Haskell and Hrushovski showing that in characteristic 0, elimination of imaginaries in the `geometric sorts’ of ACVF no longer holds if restricted exponentiation is definable.
• Logic Seminar
16 February 2012
17:00
Peter Pappas (Oxford)
Abstract
<p>This talk will be accessible to non-specialists and in particular details how model theory naturally leads to specific representations of abelian group rings as rings of global sections. The model-theoretic approach is motivated by algebraic results of Amitsur on the Semisimplicity Problem, on which a brief discussion will first be given.</p>
• Logic Seminar
9 February 2012
17:00
Mike Prest (Manchester)
Abstract
To each additive definable category there is attached its category of pp-imaginaries. This is abelian and every small abelian category arises in this way. The connection may be expressed as an equivalence of 2-categories. We describe two associated spectra (Ziegler and Zariski) which have arisen in the model theory of modules.
• Logic Seminar
2 February 2012
17:00
Alessandro Berarducci (Pisa)
Abstract
• Logic Seminar