Submission date: 10 July 2024

Abstract:

Let T be the theory of an o-minimal field and T_0 a common reduct of T and T_{an}.
I adapt Mourgues' and Ressayre's constructions to deduce structure results for T_0-reducts of T-λ-spherical completion of models of T_{convex}.
These in particular entail that whenever ℝ_L is a reduct of ℝ_{an,exp} defining the exponential, every elementary extension of ℝ_L has an elementary truncation-closed embedding in No. This partially answers a question in [3](arXiv:2002.07739).
The main technical result is that certain expansion of Hahn fields by generalized power series interpreted as functions defined on the positive infinitesimal elements, have the property that truncation closed subsets generate truncation closed substructures. This leaves room for possible generalizations to the case in which T_0 is power bounded but not necessarily a reduct of T_{an}.

Mathematics Subject Classification: 16W60, 03C64 (Primary) 12J15, 06F20, 06F25 (Secondary)

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Full text arXiv 2407.07442: pdf, ps.