A natural question to ask is whether this result has an analogue in the context of large cardinals. The purpose of this article is to provide the strongest such analogue not ruled out by limitations imposed by the existence of Woodin cardinals. To describe the latter limitations we consider the forcing P , described as follows. Let δ be inaccessible and consider the language L(δ): (a) n ∈ R bel...

We prove that a real x is 1-generic if and only if every differentiable computable function has continuous derivative at x . This provides a counterpart to recent results connecting effective notions of randomness with differentiability. We also consider multiply differentiable computable functions and polynomial time computable functions. 2010 Mathematics Subject Classification 03E15; 03F60 (p...

We study the connection between Schnorr triviality and genericity. We show that while no 2-generic is Turing equivalent to a Schnorr trivial and no 1-generic is tt-equivalent to a Schnorr trivial, there is a 1-generic that is Turing equivalent to a Schnorr trivial. However, every such 1-generic must be high. As a corollary, we prove that not all K-trivials are Schnorr trivial. We also use these...

Bruno Poizat is associated, among other things, with broadening the scope of the theory of groups of finite Morley rank to the level of stable groups [P87], in keeping with the general trend of the development of model theory from Morley to Shelah. But this has not prevented him from taking an active interest in such aspects of the theory as are associated more particularly with the case of fin...

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We address a fundamental question concerning spatio-temporal database systems: “What are exactly spatio-temporal queries?” We define spatio-temporal queries to be computable mappings that are also generic, meaning that the result of a query may only depend to a limited extent on the actual internal representation of the spatio-temporal data. Genericity is defined as invariance under transformat...