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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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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Tari, S. Strong cell decomposition property in o-minimal traces. Arch. Math. Logic (2020). https://doi.org/10.1007/s00153-020-00739-2
- O-minimal trace
- Irrational nonvaluational cut
- Dense pair
- Strong cell decomposition
Mathematics Subject Classification