Year: 2026
Type: article
Abstract: Suppose [Formula: see text] is elementarily equivalent to an archimedean ordered abelian group [Formula: see text] with small quotients (for all [Formula: see text], [Formula: see text] is finite). Then every stable reduct of [Formula: see text] which expands [Formula: see text] (equivalently every reduct that does not add new unary definable sets) is interdefinable with [Formula: see text]. This extends previous results on stable reducts of [Formula: see text] to (stable) reducts of elementary extensions of [Formula: see text]. In particular this holds for [Formula: see text] and [Formula: see text]. As a result we answer a question of Conant from 2018. This result is a corollary of a more general statement about expansions of weakly-minimal 1-based expansions of abelian groups with small quotients preserving the acl operator.
Source: Journal of Mathematical Logic
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4405434152