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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
6
votes
Non-definability of graph 3-colorability in first-order logic
It’s worth noting that Joel’s great answer says that $n$-colorability is not definable by a single sentence of first-order logic. However, it is definable by a first-order theory.. That is, for each …