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    Isomorphic extensions and applications

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    If π:(X,T)→(Z,S)\pi:(X,T)\to(Z,S) is a topological factor map between uniquely ergodic topological dynamical systems, then (X,T)(X,T) is called an isomorphic extension of (Z,S)(Z,S) if π\pi is also a measure-theoretic isomorphism. We consider the case when the systems are minimal and we pay special attention to equicontinuous (Z,S)(Z,S). We first establish a characterization of this type of isomorphic extensions in terms of mean equicontinuity, and then show that an isomorphic extension need not be almost one-to-one, answering questions of Li, Tu and Ye.Comment: 16 page

    On arithmetic models and functoriality of Bost-Connes systems

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    Denotational, Causal, and Operational Determinism in Event Structures

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    Determinism is a theoretically and practically important concept in labelled transition systems and trees. We study its generalisation to event structures. It turns out that the result depends on what characterising property of tree determinism one sets out to generalise. We present three distinct notions of event structure determinism, and show that none of them shares all the pleasant properties of the one concept for trees
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