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Coverings by open cells

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Abstract

We prove that in a semi-bounded o-minimal expansion of an ordered group every non-empty open definable set is a finite union of open cells.

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Authors and Affiliations

  1. Universidade Aberta, Campus do Tagus Park, Edifício Inovação I, Av. Dr. Jaques Delors, 2740-122, Porto Salvo, Oeiras, Portugal

    Mário J. Edmundo

  2. CMAF Universidade de Lisboa, Av. Professor Gama Pinto 2, 1649-003, Lisboa, Portugal

    Mário J. Edmundo & Luca Prelli

  3. Department of Pure Mathematics, University of Waterloo, 200 University Ave West, Waterloo, ON, N2L 3G1, Canada

    Pantelis E. Eleftheriou

Authors
  1. Mário J. Edmundo
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  2. Pantelis E. Eleftheriou
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  3. Luca Prelli
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Corresponding author

Correspondence to Mário J. Edmundo.

Additional information

The first author was supported by Fundação para a Ciência e a Tecnologia, Financiamento Base 2008-ISFL/1/209. The second author was supported by the Fundação para a Ciência e a Tecnologia grant SFRH/BPD/35000/2007. The third author was supported by Marie Curie grant PIEF-GA-2010-272021. This work is part of the FCT project PTDC/MAT/101740/2008.

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Edmundo, M.J., Eleftheriou, P.E. & Prelli, L. Coverings by open cells. Arch. Math. Logic 53, 307–325 (2014). https://doi.org/10.1007/s00153-014-0367-x

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  • DOI: https://doi.org/10.1007/s00153-014-0367-x

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