# Past Logic Seminar

23 May 2008
15:15
Philipp Heironymi
Abstract
• Logic Seminar
16 May 2008
15:15
Abstract
In recent years Schanuel’s Conjecture (SC) has played a fundamental role in the Theory of Transcendental Numbers and in decidability issues. Macintyre and Wilkie proved the decidability of the real exponential field, modulo (SC), solving in this way a problem left open by A. Tarski. Moreover, Macintyre proved that the exponential subring of R generated by 1 is free on no generators. In this line of research we obtained that in the exponential ring $(\mathbb{C}, ex)$, there are no further relations except $i^2 = −1$ and $e^{i\pi} = −1$ modulo SC. Assuming Schanuel’s Conjecture we proved that the E-subring of $\mathbb{R}$ generated by $\pi$ is isomorphic to the free E-ring on $\pi$. These results have consequences in decidability issues both on $(\mathbb{C}, ex)$ and $(\mathbb{R}, ex)$. Moreover, we generalize the previous results obtaining, without assuming Schanuel’s conjecture, that the E-subring generated by a real number not definable in the real exponential field is freely generated. We also obtain a similar result for the complex exponential field.
• Logic Seminar
9 May 2008
15:15
Jochen Koenigsmann
Abstract
• Logic Seminar
2 May 2008
15:15
Franck Benoist
Abstract
I will give a few model theoretic properties for fields with a Hasse derivation which are existentially closed. I will explain how some type-definable sets allow us to understand properties of some algebraic varieties, mainly concerning their field of definition.
• Logic Seminar
7 March 2008
14:15
Abstract
I will explain the connection between Shelah's recent notion of strongly dependent theories and finite weight in simple theories. The connecting notion of a strong theory is new, but implicit in Shelah's book. It is related to absence of the tree property of the second kind in a similar way as supersimplicity is related to simplicity and strong dependence to NIP.
• Logic Seminar
6 March 2008
10:00
Nina Frohn
Abstract
• Logic Seminar
29 February 2008
14:15
Alexey Muranov
Abstract
Bardakov and Tolstykh have recently shown that Richard Thompson's group $F$ interprets the Arithmetic $(\mathbb Z,+,\times)$ with parameters. We consider a class of infinite groups of piecewise affine permutations of an interval which contains all the three groups of Thompson and some classical families of finitely presented infinite simple groups. We have interpreted the Arithmetic in all the groups of this class. In particular we have obtained that the elementary theories of all these groups are undecidable. Additionally, we have interpreted the Arithmetic in $F$ and some of its generalizations without parameters. This is a joint work with Tuna Altınel.
• Logic Seminar
28 February 2008
10:00
Piotr Kowalski
Abstract
This is joint work with Assaf Hasson. We consider non-locally modular strongly minimal reducts of o-minimal expansions of reals. Under additional assumptions we show they have a Zariski structure.
• Logic Seminar
22 February 2008
14:15
Francois Loeser
Abstract
We shall present work in progress in collaboration with E. Hrushovski on the geometry of spaces of stably dominated types in connection with non archimedean geometry \`a la Berkovich
• Logic Seminar
15 February 2008
14:15
Ayhan Gunaydin
Abstract
There is a well-behaving class of dense ordered abelian groups called "regularly dense ordered abelian groups". This first order property of ordered abelian groups is introduced by Robinson and Zakon as a generalization of being an archimedean ordered group. Every dense subgroup of the additive group of reals is regularly dense. In this talk we consider subgroups of the multiplicative group, S, of all complex numbers of modulus 1. Such groups are not ordered, however they have an "orientation" on them: this is a certain ternary relation on them that is invariant under multiplication. We have a natural correspondence between oriented abelian groups, on one side, and ordered abelian groups satisfying a cofinality condition with respect to a distinguished positive element 1, on the other side. This correspondence preserves model-theoretic relations like elementary equivalence. Then we shall introduce a first-order notion of "regularly dense" oriented abelian group; all infinite subgroups of S are regularly dense in their induced orientation. Finally we shall consider the model theoretic structure (R,Gamma), where R is the field of real numbers, and Gamma is dense subgroup of S satisfying the Mann property, interpreted as a subset of R^2. We shall determine the elementary theory of this structure.
• Logic Seminar