On semibounded expansions of ordered groups

• Autorzy: Eleftheriou Pantelis E. , Savatovsky Alex

Identyfikatory

DOI

10.4064/ba230725-27-9

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

o-minimality; tame expansions; d-minimality; smooth functions

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2023
• Tom: Vol. 71, no 2
• Strony: 97--114
• Opis fizyczny: Bibliogr. 25 poz.

Twórcy

autor

Eleftheriou Pantelis E.

• School of Mathematics, University of Leeds, Leeds LS2 9JT, UK

autor

Savatovsky Alex

• Department of Mathematics, University of Haifa, Haifa, Israel

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024)