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{{Short description|Schema of axioms in set theory}} ...hema]] of [[axiom]]s which is a restriction of the usual [[axiom schema of separation]] in [[Zermelo–Fraenkel set theory]]. ...

...points has (''a,c'') and (''b,d'') as separating pairs. This '''point-pair separation''' is an invariant of projectivities of the line. The point-pair separation of points was written AC//BD by [[H. S. M. Coxeter]] in his textbook ''The ...

{{Separation axioms}} ...ticular, every Hausdorff space is weak Hausdorff. As a [[separation axiom|separation property]], it is stronger than T₁, which is equivalent to the s ...

...c=page 68, axiom II (2)}} introduced the axiom of adjunction as one of the axioms for a system of set theory that he introduced in about 1929. ...(<math>{\mathsf{Q}}</math>) can be interpreted in a weak set theory whose axioms are extensionality, the existence of the empty set, and the axiom of adjunc ...

...he theory of graphoids characterizes these properties in a finite set of [[axioms]] that are common to informational irrelevance and its graphical representa ...tribution whenever node set ''Z'' separates ''X'' from ''Y'' in the graph. Axioms for conditional independence in probability were derived earlier by [[A. Ph ...

...all models of a certain second-order version of the [[ZFC|Zermelo-Fraenkel axioms of set theory]] are isomorphic to a member of a certain class of sets. ...ond-order version of [[Zermelo set theory]] with a second-order version of separation, there exist models not isomorphic to any <math>V_\delta</math> for a limit ...

...as [[perfectly normal space]]s, and satisfy the strongest of [[separation axioms]]. ...

...o played by the [[axiom of extensionality]]. The subtleties the latter two axioms introduce are discussed further below. ...d simplicity, the section supposes a constructive set theory with ''full'' Separation, i.e. we allow for comprehension involving ''any'' proposition <math>P</mat ...

* '''Tameness can be seen as a topological separation principle''':<ref>{{harvnb|Lieberman|2011}}, Proposition 4.1.</ref> An AEC ...ite arXiv | last1=Boney | first1=Will | title=Tameness from large cardinal axioms | eprint=1303.0550v4 | year=2014 | class=math.LO }} ...

{{short description|Any individual whose preferences satisfy four axioms has a utility function}}{{Economics sidebar}} ...any individual whose [[preference (economics)|preferences]] satisfied four axioms has a [[utility function]], where such an individual's preferences can be r ...

* [[Separation of concerns]]: The degree to which the component under test has a single, w Treating the requirement as axioms, testability can be treated via asserting existence of a function <math> F_ ...

...]<ref name=":0">{{Cite journal|last=Tverberg|first=Helge|date=1979|title=A separation property of plane convex sets|journal=Mathematica Scandinavica|volume=45|is ...the separator, it is possible to bound any measure which satisfies certain axioms.<ref name=Chan2003 /> ...

...Luiss Publication|series=Proc. of OES/SEO 2001 Rome Workshop}}</ref>). The separation of an [[ontology]] into extremely simple [[language|linguistic]] structures ...antic decision table commitment layer that consists of the constraints and axioms of these fact types. ...

===Derivation starting from operator axioms=== ...r to the [[Operator (physics)#Operators in quantum mechanics|Hilbert space axioms of quantum mechanics]], and derive the equation of motion by specifying how ...

Like ordinary matroids, several equivalent [[Axiomatic system|systems of axioms]] exist. (Such structures that possess multiple equivalent axiomatizations === Circuit axioms === ...

...to a common ambient space X with a distance metric d satisfying all metric axioms. * '''Separation condition:''' For <math> i \in \Z </math>, the cover set <math> C_i = \{p ...

...tudy of [[geometries]] as [[axiomatic system]]s. There are several sets of axioms which give rise to [[Euclidean geometry]] or to [[non-Euclidean geometry|no ...any two points, there is just one line which passes through both of them). Axioms are assumed true, and not proven. They are the ''building blocks'' of geom ...

...collection]] This can mean either the axiom of replacement or the axiom of separation}} {{defn|no=|[[Axiom schema of predicative separation]] Axiom of separation for formulas whose quantifiers are bounded}} ...

...ry operation]]s, the "meet" and "join" operations, which must obey certain axioms; it is distributive if these two operations obey the [[distributive law]]. ...nal partial order linked with the topology via [[Priestley space|Priestley separation axiom]] can also be used to represent bounded distributive lattices. Such s ...

The notion of "function" appears as Zermelo's axiom III—the Axiom of Separation (Axiom der Aussonderung). This axiom constrains us to use a propositional f : "AXIOM III. (Axiom of separation). Whenever the propositional function Φ(''x'') is definite for all elements ...