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definability by formulas in first-order logic, e.g. as explained at https://en.wikipedia.org/wiki/Definable_set, or as in J. Robinson's first-order definition of the integers in the field of rationals

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Definability of Gödel's pairing function on ordinals

Itay Neeman has a paper Monadic Definability of Ordinals which deals with some questions related to what is definable in monadic second order logic in $\left<\mathrm{On}; <\right>$. …
James E Hanson's user avatar