Simple finiteness and o-minimal structures. (Finitude simple et structures o-minimales.) (French) Zbl 1042.03030

The author announces an interesting result: that under a certain finiteness property for a family of differential algebras of real functions on real Euclidean spaces there is an o-minimal expansion of the ordered field of real numbers in which all these functions are definable. However the key step of his proof is based on a lemma without conclusion (“Lemme 5” in the paper). It would be interesting if the author would provide a complete version of his work.


03C64 Model theory of ordered structures; o-minimality
14P10 Semialgebraic sets and related spaces
14P15 Real-analytic and semi-analytic sets
Full Text: DOI


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