  The standard treatment of sets and definable classes in first-order
Zermelo-Fraenkel set theory accords in many respects with the Fregean
foundational framework, such as the distinction between objects and concepts.
Nevertheless, in set theory we may define an explicit association of definable
classes with set objects $F\mapsto\varepsilon F$ in such a way, I shall prove,
to realize Frege's Basic Law V as a ZF theorem scheme, Russell notwithstanding.
A similar analysis applies to the Cantor-Hume principle and to Fregean
abstraction generally. Because these extension and abstraction operators are
definable, they provide a deflationary account of Fregean abstraction, one
expressible in and reducible to set theory -- every assertion in the language
of set theory allowing the extension and abstraction operators $\varepsilon F$,
$\# G$, $\alpha H$ is equivalent to an assertion not using them. The analysis
thus sidesteps Russell's argument, which is revealed not as a refutation of
Basic Law~V as such, but rather as a version of Tarski's theorem on the
nondefinability of truth, showing that the proto-truth-predicate "$x$ falls
under the concept of which $y$ is the extension" is not expressible.
