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Lattices in Locally Definable Subgroups of $langleR^{n},+rangle$

Pantelis E. Eleftheriou & Ya’Acov Peterzil

Notre Dame Journal of Formal Logic 54 (3-4):449-461 (2013)

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Definable homomorphisms of abelian groups in o-minimal structures.Ya'acov Peterzil & Sergei Starchenko - 1999 - Annals of Pure and Applied Logic 101 (1):1-27.details We investigate the group of definable homomorphisms between two definable abelian groups A and B, in an o-minimal structure . We prove the existence of a “large”, definable subgroup of . If contains an infinite definable set of homomorphisms then some definable subgroup of B admits a definable multiplication, making it into a field. As we show, all of this can be carried out not only in the underlying structure but also in any structure definable in. Download Export citation Bookmark 16 citations
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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