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Green Points in the Reals: A Strongly Dependent Expansion of a Real Closed Field

A real-field analogue of Poizat's green points, built by the Hrushovski construction as an expansion of a real closed field by a divisible multiplicative subgroup. The resulting theory is strongly dependent and has an o-minimal open core (every definable open set is semialgebraic), and the real field expanded by a dense family of logarithmic spirals (Zilber's proposal) is shown to be a model under a Schanuel-type assumption.

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GREEN POINTS IN THE REALS YILONG ZHANG Abstract. We construct an expansion of a real closed field

This model-theory paper constructs a real-field analogue of Poizat's theory of green points. Poizat used the Hrushovski construction (a Fraisse-style amalgamation restricted to 'strong' embeddings wi…