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Creators/Authors contains: "Ramsey, Nicholas"

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  1. ; ; ; (, Journal of Algebra)
    Free, publicly-accessible full text available January 15, 2026
  2. ; (, Model Theory)
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  3. ; ; (, Forum of Mathematics, Sigma)
    Abstract We initiate a systematic study ofgeneric stability independenceand introduce the class oftreeless theoriesin which this notion of independence is particularly well behaved. We show that the class of treeless theories contains both binary theories and stable theories and give several applications of the theory of independence for treeless theories. As a corollary, we show that every binary NSOP$$_{3}$$theory is simple. 
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  4. ; ; (, The Journal of Symbolic Logic)
    Abstract We develop the theory of Kim-independence in the context of NSOP $$_{1}$$ theories satisfying the existence axiom. We show that, in such theories, Kim-independence is transitive and that -Morley sequences witness Kim-dividing. As applications, we show that, under the assumption of existence, in a low NSOP $$_{1}$$ theory, Shelah strong types and Lascar strong types coincide and, additionally, we introduce a notion of rank for NSOP $$_{1}$$ theories. 
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  5. ; ; ; ; ; ; (, Journal of Mathematical Logic)
    We give examples of (i) a simple theory with a formula (with parameters) which does not fork over [Formula: see text] but has [Formula: see text]-measure 0 for every automorphism invariant Keisler measure [Formula: see text] and (ii) a definable group [Formula: see text] in a simple theory such that [Formula: see text] is not definably amenable, i.e. there is no translation invariant Keisler measure on [Formula: see text]. We also discuss paradoxical decompositions both in the setting of discrete groups and of definable groups, and prove some positive results about small theories, including the definable amenability of definable groups. 
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