Closed ordinal Ramsey numbers are a topological variant of the classical (ordinal) Ramsey numbers. We compute the exact value of the closed ordinal Ramsey number R cl (ω 2 , 3) = ω 6 .

Let Mn denote the structure obtained from Hrushovski's (non collapsed) construction with an n-ary relation and PG(Mn) its associated pregeometry. It was shown in [4] that PG(M 3 ) ∼ = PG(M 4 ). We show that M 3 has a reduct, M clq such that PG(M 4 ) ∼ = PG(M clq ). To achieve this we show that M clq is a slightly generalised Fraïssé-Hrushovski limit incorporating into the construction non-eliminable imaginary sorts in M clq .

We build a new spectrum of recursive models ( $ \operatorname {\mathrm {SRM}}(T)$ ) of a strongly minimal theory. This theory is non-disintegrated, flat, model complete, and in a language with a finite signature.

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