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arXiv · 1812.05547

Expansions of the real field by canonical products

Chris Miller·Patrick Speissegger
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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 $\mathbb{Z}$.

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Chris Miller, Patrick Speissegger. 2018-12-13. Expansions of the real field by canonical products. https://doi.org/10.4153/s0008439519000572

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