WHEN IS SCALAR MULTIPLICATION DECIDABLE? - U.I.U.C. Math

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WHEN IS SCALAR MULTIPLICATION DECIDABLE? PHILIPP HIERONYMI

Abstract. Let K be a subfield of R. The theory of the ordered K-vector space R expanded by a predicate for Z is decidable if and only if K is a real quadratic field.

1. Introduction It has long been known that the first order theory of the structure (R,