Eleftheriou, P.E. and Savatovsky, A. (2023) On semibounded expansions of ordered groups. Bulletin of the Polish Academy of Sciences: Mathematics. ISSN 0239-7269
Abstract
We explore semibounded expansions of arbitrary ordered groups; namely, expansions that do not define a field on the whole universe. We show that if R=⟨R,<,+,…⟩ is a semibounded o-minimal structure and P⊆R is a set satisfying certain tameness conditions, then ⟨R,P⟩ remains semibounded. Examples include the cases when R=⟨R,<,+,(x↦λx)λ∈R,⋅↾[0,1]2⟩, and P=2Z or P is an iteration sequence. As an application, we show that smooth functions definable in such ⟨R,P⟩ are definable in R.
Metadata
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Copyright, Publisher and Additional Information: | © Instytut Matematyczny PAN, 2023. This is an author produced version of an article published in Bulletin of the Polish Academy of Sciences: Mathematics. Uploaded in accordance with the publisher's self-archiving policy. | ||||
Keywords: | o-minimality, tame expansions, d-minimality, smooth functions | ||||
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Institution: | The University of Leeds | ||||
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) | ||||
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Depositing User: | Symplectic Publications | ||||
Date Deposited: | 11 Oct 2023 15:26 | ||||
Last Modified: | 15 Nov 2023 16:24 | ||||
Status: | Published online | ||||
Publisher: | Instytut Matematyczny | ||||
Identification Number: | https://doi.org/10.4064/ba230725-27-9 |