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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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
- O-minimal structures
- Open cells
- Semi-bounded structures
Mathematics Subject Classification (2010)