In mathematics, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is one of several axiomatic systems that were proposed in the early twentieth century to formulate a theory of sets free of paradoxes such as Russell's paradox. Zermelo–Fraenkel set theory with the historically controversial axiom of choice included is commonly abbreviated ZFC, where C stands for choice (Ciesielski 1997). Many authors use ZF to refer to the axioms of Zermelo–Fraenkel set theory with the axiom of choice excluded. Today ZFC is the standard form of axiomatic set theory and as...
As far as I can make out, the quantum part of the Chronology Protection Conjecture hinges on the fact that in curved space, in the semiclassical approximation, the stress energy tensor contains a term
\begin{equation}
\lim_{x\rightarrow y}\sum_{\gamma \neq \gamma_0} \frac{\sqrt{\Delta_\gamma (x...
In set theory and its applications throughout mathematics, a class is a collection of sets (or sometimes other mathematical objects) that can be unambiguously defined by a property that all its members share. The precise definition of "class" depends on foundational context. In work on Zermelo–Fraenkel set theory, the notion of class is informal, whereas other set theories, such as Von Neumann–Bernays–Gödel set theory, axiomatize the notion of "proper class", e.g., as entities that are not members of another entity.
A class that is not a set (informally in Zermelo–Fraenkel) is called a proper class...
