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A semi-linear group which is not affine

Pantelis E. Eleftheriou

Annals of Pure and Applied Logic 156 (2):287-289 (2008)

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Non-standard lattices and o-minimal groups.Pantelis E. Eleftheriou - 2013 - Bulletin of Symbolic Logic 19 (1):56-76.details We describe a recent program from the study of definable groups in certain o-minimal structures. A central notion of this program is that of a lattice. We propose a definition of a lattice in an arbitrary first-order structure. We then use it to describe, uniformly, various structure theorems for o-minimal groups, each time recovering a lattice that captures some significant invariant of the group at hand. The analysis first goes through a local level, where a pertinent notion of pregeometry and (...) Download Export citation Bookmark
Locally definable homotopy.Elías Baro & Margarita Otero - 2010 - Annals of Pure and Applied Logic 161 (4):488-503.details In [E. Baro, M. Otero, On o-minimal homotopy, Quart. J. Math. 15pp, in press ] o-minimal homotopy was developed for the definable category, proving o-minimal versions of the Hurewicz theorems and the Whitehead theorem. Here, we extend these results to the category of locally definable spaces, for which we introduce homology and homotopy functors. We also study the concept of connectedness in -definable groups — which are examples of locally definable spaces. We show that the various concepts of connectedness associated (...) Download Export citation Bookmark 4 citations
Locally definable homotopy.Elías Baro & Marg\ Otero - 2010 - Annals of Pure and Applied Logic 161 (4):488-503.details In [E. Baro, M. Otero, On o-minimal homotopy, Quart. J. Math. 15pp, in press ] o-minimal homotopy was developed for the definable category, proving o-minimal versions of the Hurewicz theorems and the Whitehead theorem. Here, we extend these results to the category of locally definable spaces, for which we introduce homology and homotopy functors. We also study the concept of connectedness in -definable groups — which are examples of locally definable spaces. We show that the various concepts of connectedness associated (...) Download Export citation Bookmark 4 citations

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