Premium
Product cones in dense pairs
Author(s) -
Eleftheriou Pantelis E.
Publication year - 2022
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.202100028
Subject(s) - mathematics , cone (formal languages) , product (mathematics) , set (abstract data type) , decomposition , pure mathematics , field (mathematics) , combinatorics , geometry , algorithm , computer science , ecology , biology , programming language
LetM = ⟨ M , < , + , ⋯ ⟩ $\mathcal {M}=\langle M, <, +, \dots \rangle$ be an o‐minimal expansion of an ordered group, andP ⊆ M $P\subseteq M$ a dense set such that certain tameness conditions hold. We introduce the notion of a product cone inM ∼ = ⟨ M , P ⟩ $\widetilde{\mathcal {M}}=\langle \mathcal {M}, P\rangle$ , and prove: if M $\mathcal {M}$ expands a real closed field, thenM ∼ $\widetilde{\mathcal {M}}$ admits a product cone decomposition. If M $\mathcal {M}$ is linear, then it does not. In particular, we settle a question from [10].