Geodesic
A partial order where all monotone maps are definable
Fundamenta Mathematicae, Tome 152 (1997) no. 3, pp. 255-265
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It is consistent that there is a partial order (P,≤) of size $ℵ_1$ such that every monotone function f:P → P is first order definable in (P,≤). 
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Martin Goldstern; Saharon Shelah. A partial order where all monotone maps are definable. Fundamenta Mathematicae, Tome 152 (1997) no. 3, pp. 255-265. doi: 10.4064/fm-152-3-255-265

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