Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network

  Advanced Search  

Archive for Mathematical Logic manuscript No. (will be inserted by the editor)

Summary: Archive for Mathematical Logic manuscript No.
(will be inserted by the editor)
Vincent Astier
Elementary equivalence of some rings of
definable functions
Received: date / Revised: date
Abstract We characterize elementary equivalences and inclusions between von
Neumann regular real closed rings in terms of their boolean algebras of idempo-
tents, and prove that their theories are always decidable. We then show that, under
some hypotheses, the map sending an L-structure R to the L-structure of definable
functions from Rn to R preserves elementary inclusions and equivalences and gives
a structure with a decidable theory whenever R is decidable. We briefly consider
structures of definable functions satisfying an extra condition such as continuity.
Keywords von Neumann regular ring elementary equivalence ring of definable
Mathematics Subject Classification (2000) 03C60 06F25 14P10
1 Introduction and notation
Let L be a first-order language. If R is an L-structure and n N, we consider
defL(Rn,R) the set of L-definable maps from Rn to R, which can be seen as an L-
structure via its inclusion in RRn


Source: Astier, Vincent - Department of Mathematics, University College Dublin


Collections: Mathematics