Past Logic Seminar

7 March 2013
17:00
Jeff Paris
Abstract
I shall give a non-technical survey of Pure Inductive Logic, a branch of Carnap's Inductive Logic which was anticipated early on in that subject but has only recently begun to be developed as an area of Mathematical Logic. My intention is to cover its origins and aims, and to pick out some of the key concepts which have emerged in the last decade or so.
28 February 2013
17:00
Gareth Jones
Abstract
Masser recently proved a bound on the number of rational points of bounded height on the graph of the zeta function restricted to the interval [2,3]. Masser's bound substantially improves on bounds obtained by Bombieri-Pila-Wilkie. I'll discuss some results obtained in joint work with Gareth Boxall in which we prove bounds only slightly weaker than Masser's for several more natural analytic functions.
21 February 2013
17:00
Ivan Tomasic
Abstract
The study of difference algebraic geometry stems from the efforts of Macintyre and Hrushovski to count the number of solutions to difference polynomial equations over fields with powers of Frobenius. We propose a notion of multiplicity in the context of difference algebraic schemes and prove a first principle of preservation of multiplicity. We shall also discuss how to formulate a suitable intersection theory of difference schemes.
7 February 2013
17:00
Peter Holy
Abstract
<p>The Outer Model Programme investigates L-like forcing &nbsp;extensions of the universe, where we say that a model of Set Theory &nbsp;is L-like if it satisfies properties of Goedel's constructible&nbsp;universe of sets L. I will introduce the Outer Model Programme, talk &nbsp;about its history, motivations, recent results and applications. I &nbsp;will be presenting joint work with Sy Friedman and Philipp Luecke.</p>
6 December 2012
17:00
George Metcalfe
Abstract
(Joint work with Nikolaos Galatos.) Proof-theoretic methods provide useful tools for tackling problems for many classes of algebras. In particular, Gentzen systems admitting cut-elimination may be used to establish decidability, complexity, amalgamation, admissibility, and generation results for classes of residuated lattices corresponding to substructural logics. However, for classes of algebras bearing a family resemblance to groups, such methods have so far met only with limited success. The main aim of this talk will be to explain how proof-theoretic methods can be used to obtain new syntactic proofs of two core theorems for the class of lattice-ordered groups: namely, Holland's result that this class is generated as a variety by the lattice-ordered group of order-preserving automorphisms of the real numbers, and the decidability of the word problem for free lattice-ordered groups.
29 November 2012
17:00
Martin Hils
Abstract
(Joint work with Artem Chernikov.) In the talk, we will first recall some basic results on valued difference fields, both from an algebraic and from a model-theoretic point of view. In particular, we will give a description, due to Hrushovski, of the theory VFA of the non-standard Frobenius acting on an algebraically closed valued field of residue characteristic 0, as well as an Ax-Kochen-Ershov type result for certain valued difference fields which was proved by Durhan. We will then present a recent work where it is shown that VFA does not have the tree property of the second kind (i.e., is NTP2); more generally, in the context of the Ax-Kochen-Ershov principle mentioned above, the valued difference field is NTP2 iff both the residue difference field and the value difference group are NTP2. The property NTP2 had already been introduced by Shelah in 1980, but only recently it has been shown to provide a fruitful ‘tameness’ assumption, e.g. when dealing with independence notions in unstable NIP theories (work of Chernikov-Kaplan).

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