A fun wrinkle is that there are (infinitely many) models of set theory which are pointwise definable. Thus in the right model of zfc, every mathematical object

A fun wrinkle is that there are (infinitely many) models of set theory which are pointwise definable. Thus in the right model of zfc, every mathematical object is uniquely addressable by a certain finite formula. (see https://arxiv.org/pdf/1105.4597.pdf https://arxiv.org/pdf/1105.4597.pdf )