Strong cell decomposition property in o-minimal traces

Abstract

Strong cell decomposition property has been proved in non-valuational weakly o-minimal expansions of ordered groups. In this note, we show that all o-minimal traces have strong cell decomposition property. Also after introducing the notion of irrational nonvaluational cut in arbitrary o-minimal structures, we show that every expansion of o-minimal structures by irrational nonvaluational cuts is an o-minimal trace.

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Acknowledgements

This research was in part supported by a grant from IPM (No. 96030031). The author thank the anonymous reviewers whose useful comments helped to improve the paper.

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Correspondence to Somayyeh Tari.

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Tari, S. Strong cell decomposition property in o-minimal traces. Arch. Math. Logic (2020). https://doi.org/10.1007/s00153-020-00739-2

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Keywords

  • O-minimal trace
  • Irrational nonvaluational cut
  • Dense pair
  • Strong cell decomposition

Mathematics Subject Classification

  • 03C64