On Thursday the 17-th of February, 2022, Dan Segal (All Souls College, Oxford) will give an online talk “Groups, rings, logic” at 20:00 Novosibirsk time (13:00 London time).
Abstract: In group theory, interesting statements about a group usually can’t be expressed in the language of first-order logic. It turns out, however, that some groups can actually be determined by their first-order properties, or, even more strongly, by a single first-order sentence. In the latter case the group is said to be finitely axiomatizable. I will describe some examples of this phenomenon (joint work with A. Nies and K. Tent). One family of results concerns axiomatizability of p-adic analytic pro-p groups, within the class of all profinite groups. Another main result is that for an adjoint simple Chevalley group of rank at least 2 and an integral domain R; the group G(R) is bi-interpretable with the ring R. This means in particular that first-order properties of the group G(R) correspond to first-order properties of the ring R. As many rings are known to be finitely axiomatizable we obtain the corresponding result for many groups; this holds in particular for every finitely generated group of the form G(R).
Chair of the session: Evgeny Khukhro
The link to the Zoom meeting: https://us02web.zoom.us/j/3167567840?pwd=aExXZmUxVmE5blYxYTVRMHhrakxuQT09
(ID 316 756 7840, Password gD11t2).
See the program updates at http://mca.nsu.ru/kourovkaforum/.
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