replacement axiom
1replacement, axiom of — The axiom added to Zermelo s set theory by A. A. Fraenkel (1891–1965), to produce the classical set theory known as ZF. Put in terms of second order logic, the axiom states that any function whose domain is a set has a range which is also a set.… …
2replacement — replacement, axiom of …
3Replacement — means: * Axiom schema of replacement * Text replacement, a feature of word processors correcting automatically common misspellings and typos * Replacement rate * Sampling (statistics) with replacementee also*Replacements …
4Axiom schema of replacement — In set theory, the axiom schema of replacement is a schema of axioms in Zermelo Fraenkel set theory (ZFC) that asserts that the image of any set under any definable mapping is also a set. It is necessary for the construction of certain infinite… …
5Axiom schema of specification — For the separation axioms in topology, see separation axiom. In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom schema of specification, axiom schema of separation, subset axiom scheme or… …
6Axiom of empty set — In set theory, the axiom of empty set is one of the axioms of Zermelo–Fraenkel set theory and one of the axioms of Kripke–Platek set theory. Formal statement In the formal language of the Zermelo–Fraenkel axioms, the axiom reads::exist x, forall… …
7Axiom of limitation of size — In class theories, the axiom of limitation of size says that for any class C , C is a proper class (a class which is not a set (an element of other classes)) if and only if V (the class of all sets) can be mapped one to one into C .:forall C… …
8Axiom schema — In mathematical logic, an axiom schema generalizes the notion of axiom.An axiom schema is a formula in the language of an axiomatic system, in which one or more schematic variables appear. These variables, which are metalinguistic constructs,… …
9Axiom of regularity — In mathematics, the axiom of regularity (also known as the axiom of foundation) is one of the axioms of Zermelo Fraenkel set theory and was introduced by harvtxt|von Neumann|1925. In first order logic the axiom reads::forall A (exists B (B in A)… …
10Axiom of pairing — In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of pairing is one of the axioms of Zermelo Fraenkel set theory. Formal statement In the formal language of the Zermelo Frankel axioms, the …
