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 what I do not understand (and have something to say), model theory
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
This is a non-standard paper, containing some problems, mainly in model theory, which I have, in various degrees, been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me, sometimes the problems are presented with a discussion of how I have tried to solve them, and sometimes with failed tries, anecdote and opinion. So the discussion is quite personal, in other words, egocentric and somewhat accidental. As we discuss many problems, history and side references are erratic, usually kept at a minimum ("See..." means: see the references there and possibly the paper itself). The base were lectures in Rutgers Fall '97 and reflect my knowledge then. The other half, math.LO/9906113, concentrating on set theory, is in print, but the two halves are independent. We thank A. Blass, G. Cherlin and R. Grossberg for some corrections.
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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
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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.
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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