axiom of separation

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• Axiom 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… …   Wikipedia

• Axiom 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)… …   Wikipedia

• separation, axiom of — Also known as the Aussonderungsaxiom . The unrestricted principle of comprehension leads to contradiction in set theory . The axiom of separation, due to Zermelo, restored consistency by allowing a set of objects to exist when it is the subset of …   Philosophy dictionary

• Separation — may refer to several different subjects: *Separation processes, in chemistry *Flow separation, separation of a fluid boundary layer from the surface of a solid body moving relative to the fluid *Legal separation, a legal status where married… …   Wikipedia

• Separation logic — Separation Logic, a term attributed to John C. Reynolds, is an extension of Hoare logic that describes variations on program logic in computer science.In particular, separation logic facilitates reasoning about:* programs that manipulate pointer… …   Wikipedia

• Axiom 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… …   Wikipedia

• Axiom 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… …   Wikipedia

• Separation axiom — In topology and related fields of mathematics, there are several restrictions that one often makes on the kinds of topological spaces that one wishes to consider. Some of these restrictions are given by the separation axioms. These are sometimes… …   Wikipedia

• Axiom schema of predicative separation — In axiomatic set theory, the axiom schema of predicative separation, or of restricted, or Delta;0 separation, is a schema of axioms which is a restriction of the usual axiom schema of separation in Zermelo Fraenkel set theory. It only asserts the …   Wikipedia

• History of the separation axioms — In general topology, the separation axioms have had a convoluted history, with many competing meanings for the same term, and many competing terms for the same concept. Origins Before the current general definition of topological space, there… …   Wikipedia

• axioms of separation — separation, axiom of …   Philosophy dictionary