Axiom Collection series of albums are compilations from the Axiom record label released between 1991 and 1996. The first collection, Illuminations, collects...

mathematics, the axiom of choice, abbreviated AC or AoC, is an axiom of set theory equivalent to the statement that a Cartesian product of a collection of non-empty...

In set theory, the axiom schema of replacement is a schema of axioms in Zermelo–Fraenkel set theory (ZF) that asserts that the image of any set under...

axiom of choice included is abbreviated ZFC, where C stands for "choice", and ZF refers to the axioms of Zermelo–Fraenkel set theory with the axiom of...

axiom schema of specification, also known as the axiom schema of separation (Aussonderungsaxiom), subset axiom, axiom of class construction, or axiom...

mathematical logic, the Peano axioms (/piˈɑːnoʊ/, [peˈaːno]), also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers...

An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments...

The axiom of countable choice or axiom of denumerable choice, denoted ACω, is an axiom of set theory that states that every countable collection of non-empty...

mathematics and logic, an axiomatic system is any set of primitive notions and axioms to logically derive theorems. A theory is a consistent, relatively-self-contained...

finitely many axioms, the axiom schema of class comprehension is first replaced with finitely many class existence axioms. Then these axioms are used to...

are equivalent to the axiom of choice (often called AC, see also Axiom of choice § Equivalents). Ernst Zermelo introduced the axiom of choice as an "unobjectionable...

a collection of operations on A (typically binary operations such as addition and multiplication), and a finite set of identities (known as axioms) that...

twentieth century, of which Zermelo–Fraenkel set theory (with or without the axiom of choice) is still the best-known and most studied. Set theory is commonly...

power set axiom, choice, and sometimes infinity. Also the axioms of separation and collection here are weaker than the corresponding axioms in ZFC because...

1993 – Axiom Collection II: Manifestation 1993 – Divination – Ambient Dub Volume 1 1994 – Axiom Ambient – Lost in the Translation 1995 – Axiom Funk –...

In mathematics, the gluing axiom is introduced to define what a sheaf F {\displaystyle {\mathcal {F}}} on a topological space X {\displaystyle X} must...

In mathematics, the axiom of power set is one of the Zermelo–Fraenkel axioms of axiomatic set theory. It guarantees for every set x {\displaystyle x} the...

second-countable space is said to satisfy the second axiom of countability. Like other countability axioms, the property of being second-countable restricts...

Bryan Ferry Taxi Warner Bros. 1993 Various Artists Manifestation: Axiom Collection II PolyGram 1993 James Brown Soul Pride: The Instrumentals (1960–1969)...

Axiom Verge 2 is a Metroidvania video game by American indie developer Thomas Happ Games. It is the sequel to Axiom Verge and was released on August 11...

the real numbers used, completeness may take the form of an axiom (the completeness axiom), or may be a theorem proven from the construction. There are...

Reality Mix" was included on Axiom Collection: Manifestation. "Playin' with Fire" was issued as a 12" single in 1992 (Axiom/Island, 422-866 499-1) featuring...

for any x, the collection of all y such that yRx is a set.) Proofs or constructions using induction and recursion often use the axiom of choice to produce...

given collection. In Section 1 Halmos writes that "to avoid terminological monotony, we shall sometimes say collection instead of set." Hence this axiom is...

In mathematical physics, the Wightman axioms (also called Gårding–Wightman axioms), named after Arthur Wightman, are an attempt at a mathematically rigorous...

(with cardinality ℵ0) of positive integers. If the axiom of countable choice (a weaker version of the axiom of choice) holds, then ℵ0 is smaller than any other...

list of releases by Material. 1991: Axiom Collection: Illuminations – contains "Cosmic Slop" 1993: Axiom Collection II: Manifestation – contains "Mantra"...

up garbage. He is visited by a robot called EVE sent from the starship Axiom, with whom he falls in love and pursues across the galaxy. After directing...

Bryan Ferry Taxi Warner Bros. 1993 Various Artists Manifestation: Axiom Collection II PolyGram 1993 James Brown Soul Pride: The Instrumentals (1960–1969)...

where distinct points have disjoint neighbourhoods. Of the many separation axioms that can be imposed on a topological space, the "Hausdorff condition" (T2)...