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On the first-order expressibility of lattice properties related to unicoherence in continua

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Abstract

Many properties of compacta have “textbook” definitions which are phrased in lattice-theoretic terms that, ostensibly, apply only to the full closed-set lattice of a space. We provide a simple criterion for identifying such definitions that may be paraphrased in terms that apply to all lattice bases of the space, thereby making model-theoretic tools available to study the defined properties. In this note we are primarily interested in properties of continua related to unicoherence; i.e., properties that speak to the existence of “holes” in a continuum and in certain of its subcontinua.

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  1. Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, WI, 53201-1881, USA

    Paul Bankston

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  1. Paul Bankston
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Correspondence to Paul Bankston.

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Bankston, P. On the first-order expressibility of lattice properties related to unicoherence in continua. Arch. Math. Logic 50, 503–512 (2011). https://doi.org/10.1007/s00153-011-0229-8

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  • DOI: https://doi.org/10.1007/s00153-011-0229-8

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