Zermelo set theory, as set out in an important paper in 1908 by Ernst Zermelo, is the ancestor of modern set theory. It bears certain differences from its descendants, which are not always understood, and are frequently misquoted. This article sets out the original axioms, with the original text (translated into English) and original numbering.
Other articles related to "set theory, sets, set, theory, zermelo set theory, zermelo":
... properties as well as its consequences in descriptive set theory ... Determinacy of closed sets of Aω for arbitrary A is equivalent to the axiom of choice over ZF (Kechris 1995, p ... When working in set-theoretical systems where the axiom of choice is not assumed, this can be circumvented by considering generalized strategies known as ...
... various "strong axioms of infinity" to our usual base theory, NFU + Infinity + Choice ... This base theory, known consistent, has the same strength as TST + Infinity, or Zermelo set theory with Separation restricted to bounded formulas (Mac ... One can add to this base theory strong axioms of infinity familiar from the ZFC context, such as "there exists an inaccessible cardinal," but it is more ...
... Zermelo's paper is notable for what may be the first mention of Cantor's theorem explicitly and by name ... This appeals strictly to set theoretical notions, and is thus not exactly the same as Cantor's diagonal argument ... Cantor's theorem "If M is an arbitrary set, then always M < P(M) ...
Famous quotes containing the words theory and/or set:
“No theory is good unless it permits, not rest, but the greatest work. No theory is good except on condition that one use it to go on beyond.”
—André Gide (18691951)
“Some people appear to be more meager in talent than they are, just because the tasks they set themselves are always too great.”
—Friedrich Nietzsche (18441900)