2021/10/24 by Alex Savatovsky, Savatovsky, Alex
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2110.12407
openalex publication_date 2021/10/24 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We explore \semibounded expansions of arbitrary ordered groups; namely,\nexpansions that do not define a field on the whole universe. We introduce the\nnotion of a \semibounded expansion of an arbitrary ordered group,\nextending the usual notion from the o-minimal setting. For \R=(\n\ℝ, <, +, \…), a semibounded o-minimal structure and P\⊆\n\ℝ a set satisfying certain tameness conditions, we discuss under\nwhich conditions ( mathcal R,P) defines total linear functions that are not\ndefinable in \R. Examples of such structures that does define new\ntotal linear functions include the cases when \R is a reduct of\n(\ℝ,<,+,\⋅ upharpoonright (0,1)2,(x\↦ \λ\nx)\λ\∈ I\⊆ \ℝ), and P= 2^\ℤ, or P is an\niteration sequence (for any I) or P=\ℤ, for I=\ℚ.\n