论文信息 - Groups definable in two orthogonal sorts

Groups definable in two orthogonal sorts

This work can be thought of as a contribution to the model theory of group extensions. We study the groups G which are interpretable in the disjoint union of two structures (seen as a two-sorted structure). We show that if one of the two structures is superstable of finite Lascar rank and the Lascar rank is definable, then G is an extension of a group internal to the (possibly) unstable sort by a definable normal subgroup internal to the stable sort. In the final part of the paper we show that if the unstable sort is an o-minimal expansion of the reals, then G has a natural Lie structure and the extension is a topological cover.

Alessandro Berarducci | Marcello Mamino

[1] Ya'acov Peterzil,et al. On central extensions and definably compact groups in o-minimal structures , 2008 .

[2] B. Zilber. Covers of the Multiplicative Group of an Algebraically Closed Field of Characteristic Zero , 2004 .

[3] Roman Wencel. Groups, group actions and fields definable in first-order topological structures , 2012, Math. Log. Q..

[4] Pantelis E. Eleftheriou,et al. Definable quotients of locally definable groups , 2011, 1103.4770.

[5] Discrete subgroups of locally definable groups , 2012, 1202.5649.

[6] M. Ziegler,et al. A Course in Model Theory , 2012 .

[7] Anand Pillay,et al. On groups and fields definable in o-minimal structures , 1988 .

[8] Jana Maríková. Type-definable and invariant groups in o-minimal structures , 2007, J. Symb. Log..

[9] C. Steinhorn,et al. Definable Compactness and Definable Subgroups of o‐Minimal Groups , 1999 .

[10] Alessandro Berarducci,et al. On the homotopy type of definable groups in an o-minimal structure , 2011, J. Lond. Math. Soc..

[11] A. Pillay. Geometric Stability Theory , 1996 .

[12] Daniel Lascar,et al. Ranks and definability in superstable theories , 1976 .

[13] Pantelis E. Eleftheriou,et al. The universal covering homomorphism in o-minimal expansions of groups , 2007, Math. Log. Q..

[14] A. Berarducci,et al. GROUP COVERS, o-MINIMALITY, AND CATEGORICITY , 2010, 1009.5097.

[15] Ya'acov Peterzil,et al. Interpretable groups are definable , 2014, J. Math. Log..