@article {urbaniak2009note,
	title = {A note on identity and higher-order quantification.},
	journal = {Australasian Journal of Logic},
	volume = {7},
	year = {2009},
	pages = {48{\textendash}55},
	abstract = {<p>It is a commonplace remark that the identity relation, even though not expressible in a first-order language without identity with classical set-theoretic semantics, can be dened in a language without identity, as soon as we admit second-order, set-theoretically interpreted quantiers binding predicate variables that range over all subsets of the domain. However, there are fairly simple and intuitive higher-order languages with set-theoretic semantics (where the variables range over all subsets of the domain) in which the identity relation is not denable. The point is that the denability of identity in higher-order languages not only depends on what variables range over, but also is sensitive to how predication is construed.</p>},
	author = {Urbaniak, Rafal}
}
