Submission date: 1 September 2022

Abstract:

We show that for each property P in { OP, IP, TP_1, TP_2, ATP, SOP_3 } there is a poset Σ_P such that a theory has property P if and only if some model interprets a poset in which Σ_P can be embedded. We also introduce a new property SUP, consistent with NIP_2 and implying ATP and SOP.

Mathematics Subject Classification: 03C45

Keywords and phrases:

Full text arXiv 2209.00571: pdf, ps.