Definable groups in topological differential fields

arXiv1707.07881MaRDI QIDQ6289395

Françoise Point

Publication date: 25 July 2017

Abstract: For certain theories of existentially closed topological differential fields, we show that there is a strong relationship between $mathcalLcupD$-definable sets and their $mathcalL$-reducts, where $mathcalL$ is a relational expansion of the field language and $D$ a symbol for a derivation. This enables us to associate with an $mathcalLcupD$-definable group in models of such theories, a local $mathcalL$-definable group. As a byproduct, we show that in closed ordered differential fields, one has the descending chain condition on centralisers.

Mathematics Subject Classification ID

Structure of general topological groups (22A05) Model-theoretic algebra (03C60) Differential algebra (12H05) Quantifier elimination, model completeness, and related topics (03C10) Topological fields (12Jxx)

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