Real-valued NSOP_r techniques yield that NSOP2subseteq NSOP_r for r>2, an approximate alternative between new real properties and NSOP_n collapse in NTP2, and a sharp SOP2-implies-SOP3 dichotomy for finitely forbidden weak-embedding hereditary classes.
Title resolution pending
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
fields
math.LO 2years
2026 2representative citing papers
Authors prove SOP_n is straightly definable and poset definable for n >= 4, completing the straight definability classification of classical model-theoretic properties, and show that implications between positively straightly definable properties in countably categorical theories occur at the exists
citing papers explorer
-
Some applications of the real strict order property hierarchy
Real-valued NSOP_r techniques yield that NSOP2subseteq NSOP_r for r>2, an approximate alternative between new real properties and NSOP_n collapse in NTP2, and a sharp SOP2-implies-SOP3 dichotomy for finitely forbidden weak-embedding hereditary classes.
-
On the notion of a patterning property in model theory
Authors prove SOP_n is straightly definable and poset definable for n >= 4, completing the straight definability classification of classical model-theoretic properties, and show that implications between positively straightly definable properties in countably categorical theories occur at the exists