Equivalents of Notop
Year: 2025
Type: article
Abstract: Working within the context of countable, superstable theories, we give many equivalents of a theory having NOTOP. In particular, NOTOP is equivalent to V-DI, the assertion that any type V -dominated by an independent triple is isolated over the triple. If T has NOTOP, then every model N is atomic over an independent tree of countable, elementary substructures, and hence is determined up to back-and-forth equivalence over such a tree. We also verify Shelah’s assertion from Chapter XII of [9] that NOTOP implies PMOP (without using NDOP).
Source: Journal of Symbolic Logic
Authors: MICHAEL C. LASKOWSKI, DANIELLE S. ULRICH
Institution: University of Maryland, College Park
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W4414000082