21 research outputs found

    Topological properties of definable sets in tame perfect fields

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    Let KK be a field. We continue to study the recently introduced \'etale open topology on the KK-points V(K)V(K) of a KK-variety VV. The \'etale open topology is non-discrete if and only if KK is large. If KK is separably, real, pp-adically closed then the \'etale open topology agrees with the Zariski, order, valuation topology, respectively. We show that existentially definable sets in perfect large fields behave well with respect to this topology: such sets are finite unions of \'etale open subsets of Zariski closed sets. This implies that existentially definable sets in arbitrary perfect large fields enjoy some of the well-known topological properties of definable sets in algebraically, real, and pp-adically closed fields. We introduce and study the class of \'ez fields: KK is \'ez if KK is large and every definable set is a finite union of \'etale open subsets of Zariski closed sets. This should be seen as a generalized notion of model completeness for large fields. Algebraically closed, real closed, pp-adically closed, and bounded PAC\mathrm{PAC} fields are \'ez. (In particular pseudofinite fields and infinite algebraic extensions of finite fields are \'ez.) We develop the basics of a theory of definable sets in \'ez fields. This gives a uniform approach to the theory of definable sets across all characteristic zero local fields and a new topological theory of definable sets in bounded PAC\mathrm{PAC} fields. We also show that some prominent examples of possibly non-model complete model-theoretically tame fields (characteristic zero Henselian fields and Frobenius fields) are \'ez

    Reading in Trance: Hypnosis and the Novelistic Imagination

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    This interdisciplinary study in comparative literature reconceptualizes hypnosis as an aesthetic activity in light of the phenomenology of novel reading, literary theory, and narrative ethics. It begins by tracing the history of hypnotism in the medical literature, from Mesmer, Puységur, Bernheim and Charcot to Sigmund Freud, and in nineteenth-century fiction, from Balzac, Poe, and Flaubert, to Maupassant, Doyle and Du Maurier. It then turns to contemporary literary theory to examine the common aesthetic features of the novelistic and hypnotic imaginations. Centered on the concepts of aesthetic illusion, absorption-immersion and distance, activity and performativity, it strives to correct misconceptions of the hypnotic state that still portray it as one of pure passivity and receptivity, rather than activity, co-creation, and imaginative participation. By establishing hypnosis as a narrative, rather than purely dramatic-mimetic, practice, it draws out the ethical and therapeutic value of hypnotic and novelistic narration, and the autonomy of the hypnotic-imaginative subject. The analogy between hypnosis and the act of reading fiction thus draws out similar forms of storytelling that enable an “unselfing” of the subject, opening up the individual to other lives, both actual and fictional

    Unsolved Problems in Group Theory. The Kourovka Notebook

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    This is a collection of open problems in group theory proposed by hundreds of mathematicians from all over the world. It has been published every 2-4 years in Novosibirsk since 1965. This is the 19th edition, which contains 111 new problems and a number of comments on about 1000 problems from the previous editions.Comment: A few new solutions and references have been added or update

    Multisorted modules and their model theory

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    Multisorted modules, equivalently representations of quivers, equivalently additive functors on preadditive categories, encompass a wide variety of additive structures. In addition, every module has a natural and useful multisorted extension by imaginaries. The model theory of multisorted modules works just as for the usual, 1-sorted modules. A number of examples are presented, some in considerable detail
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