Expansions of the Real Field with Power Functions

@article{Miller1994ExpansionsOT,
  title={Expansions of the Real Field with Power Functions},
  author={Chris Miller},
  journal={Ann. Pure Appl. Log.},
  year={1994},
  volume={68},
  pages={79-94}
}
  • Chris Miller
  • Published 1994
  • Mathematics, Computer Science
  • Ann. Pure Appl. Log.
Abstract We investigate expansions of the ordered field of real numbers equipped with a family of real power functions. We show in particular that the (O-minimal) theory of the ordered field of real numbers augmented by all restricted analytic functions and all real power functions admits elimination of quantifiers and has a universal axiomatization. We derive that every function of one variable definable in this structure, not ultimately identically 0, is asymptotic at + ∞ to a real function… Expand
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