The real field with an irrational power function and a dense multiplicative subgroup

  title={The real field with an irrational power function and a dense multiplicative subgroup},
  author={Philipp Hieronymi},
  journal={J. Lond. Math. Soc.},
In recent years the field of real numbers expanded by a multiplicative subgroup has been studied extensively. In this thesis, the known results will be extended to expansions of the real field. I will consider the structure R consisting of the field of real numbers and an irrational power function. Using Schanuel conditions, I will give a first-order axiomatization of expansions of R by a dense multiplicative subgroup which is a subset of the real algebraic numbers. It will be shown that every… Expand
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