Interpreting the projective hierarchy in expansions of the real line

Philipp Hieronymi, Michael Tychonievich

Research output: Contribution to journalArticlepeer-review


We give a criterion when an expansion of the ordered set of real numbers defines the image of (ℝ,+,·, ℕ) under a semialgebraic injection. In particular, we show that for a non-quadratic irrational number α, the expansion of the ordered ℚ(α)-vector space of real numbers by ℕ defines multiplication on ℝ.

Original languageEnglish (US)
Pages (from-to)3259-3267
Number of pages9
JournalProceedings of the American Mathematical Society
Issue number9
StatePublished - Sep 1 2014

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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