Submission date: 13 December 2018

Abstract:

We consider expansions of o-minimal structures on the real field by collections of restrictions to the positive real line of the canonical Weierstrass products associated to sequences such as (-n^s)_{n>0} (for s>0) and (-s^n)_{n>0} (for s>1), and also expansions by associated functions such as logarithmic derivatives. There are only three possible outcomes known for the resulting structures: (i) o-minimality; (ii) d-minimality (but not o-minimality); (iii) definability of ℤ.

Mathematics Subject Classification: Primary 03C64, Secondary 30D10, 30D15, 30D60

Keywords and phrases:

Full text arXiv 1812.05547: pdf, ps.