Expansions of o-minimal structures by fast sequences

Friedman, Harvey; Miller, Chris

J. Symbolic Logic, Tome 70 (2005) no. 1, p. 410-418 / Harvested from Project Euclid

Résumé

Let ℜ be an o-minimal expansion of (ℝ, <+) and (φ_k)_k∈ℕ be a sequence of positive real numbers such that lim_k→+∞f(φ_k)/φ_k+1=0 for every f:ℝ→ ℝ definable in ℜ. (Such sequences always exist under some reasonable extra assumptions on ℜ, in particular, if ℜ is exponentially bounded or if the language is countable.) Then (ℜ, (S)) is d-minimal, where S ranges over all subsets of cartesian powers of the range of φ.

Publié le : 2005-06-14
Classification: 03C64

@article{1120224720,
     author = {Friedman, Harvey and Miller, Chris},
     title = {Expansions of o-minimal structures by fast sequences},
     journal = {J. Symbolic Logic},
     volume = {70},
     number = {1},
     year = {2005},
     pages = { 410-418},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1120224720}
}

Friedman, Harvey; Miller, Chris. Expansions of o-minimal structures by fast sequences. J. Symbolic Logic, Tome 70 (2005) no. 1, pp.  410-418. http://gdmltest.u-ga.fr/item/1120224720/