4,565 research outputs found

    Spectropolarimetry with the DAO 1.8-m telescope

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    The fast-switching DAO spectropolarimeter mounted on the 1.8-m Plaskett telescope started operation in 2007. Almost 14,000 medium-resolution (R=15,000) polarimetric spectra of 65 O - F type stars have been obtained since then in the course of three ongoing projects: the DAO Magnetic Field Survey, supporting observations for the CFHT MiMeS survey, and an investigation of the systematic differences between the observed longitudinal field measured with the Hbeta line and metallic lines. The projects are briefly described here. The current status as well as some results are presented.Comment: "Magnetic Stars", Proceedings of the International Conference, Nizhny Arkhyz, 27 August - 1 September 201

    Degeneracy between Abelian and Non-Abelian Strings

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    In a model that supports both Abelian (Abrikosov-Nielsen-Olesen) and non-Abelian strings we analyze the parameter space to find examples in which these strings not only coexist but are degenerate in tension. We prove that both solutions are locally stable, i.e there are no negative modes in the string background. The tension degeneracy is achieved at the classical level and is expected to be lifted by quantum corrections. The set up of the model, analogous to that of Witten's superconducting cosmic strings, had been extended to include non-Abelian strings

    The weakness of the pigeonhole principle under hyperarithmetical reductions

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    The infinite pigeonhole principle for 2-partitions (RT21\mathsf{RT}^1_2) asserts the existence, for every set AA, of an infinite subset of AA or of its complement. In this paper, we study the infinite pigeonhole principle from a computability-theoretic viewpoint. We prove in particular that RT21\mathsf{RT}^1_2 admits strong cone avoidance for arithmetical and hyperarithmetical reductions. We also prove the existence, for every Δn0\Delta^0_n set, of an infinite lown{}_n subset of it or its complement. This answers a question of Wang. For this, we design a new notion of forcing which generalizes the first and second-jump control of Cholak, Jockusch and Slaman.Comment: 29 page

    Pi01 encodability and omniscient reductions

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    A set of integers AA is computably encodable if every infinite set of integers has an infinite subset computing AA. By a result of Solovay, the computably encodable sets are exactly the hyperarithmetic ones. In this paper, we extend this notion of computable encodability to subsets of the Baire space and we characterize the Π10\Pi^0_1 encodable compact sets as those who admit a non-empty Σ11\Sigma^1_1 subset. Thanks to this equivalence, we prove that weak weak K\"onig's lemma is not strongly computably reducible to Ramsey's theorem. This answers a question of Hirschfeldt and Jockusch.Comment: 9 page
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