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
Hypergraph regularity and higher arity VC -dimension
4 Pith papers cite this work. Polarity classification is still indexing.
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math.LO 4years
2026 4verdicts
UNVERDICTED 4representative citing papers
Defines FHP theories via the Fractional Helly Property as a new subclass of low NTP2 theories, provides algebraic examples, and derives partial results on forking combinatorics and two-cardinal counting functions.
Strongly n-distal NIP theories admit a hypergraph regularity lemma, compact domination for definable fsg groups, and the n-distality hierarchy is strict among stable theories; infinite such fields have characteristic zero.
The inner product on the Hilbert unit ball requires k exponential in 1/ε for (k,ε)-stability, with bounds exp(π/ε) upper and exp(log 2/ε) lower, and similar exponential scaling for nonlinear powers.
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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
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Fractional Helly property and combinatorics of forking in NTP$_2$ theories
Defines FHP theories via the Fractional Helly Property as a new subclass of low NTP2 theories, provides algebraic examples, and derives partial results on forking combinatorics and two-cardinal counting functions.
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On n-distality, n-triviality and hypergraph regularity in NIP theories
Strongly n-distal NIP theories admit a hypergraph regularity lemma, compact domination for definable fsg groups, and the n-distality hierarchy is strict among stable theories; infinite such fields have characteristic zero.
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A note on quantitative stability in Hilbert spaces
The inner product on the Hilbert unit ball requires k exponential in 1/ε for (k,ε)-stability, with bounds exp(π/ε) upper and exp(log 2/ε) lower, and similar exponential scaling for nonlinear powers.