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WIKIMEDIA DISAMBIGUATION PAGE

Linear Correspondence Axiom; Antisymmetry Theory

Axiom schema

A FORMULA IN THE METALANGUAGE OF AN AXIOMATIC SYSTEM IN WHICH ONE OR MORE SCHEMATIC VARIABLES APPEAR

Axiom scheme; Axiom schemata; Axiom-scheme; Finite axiomatization

In mathematical logic, an axiom schema (plural: axiom schemata or axiom schemas) generalizes the notion of axiom.

https://en.wikipedia.org/wiki/Axiom_schema

Axiom of extensionality

AXIOM OF ZERMELO–FRAENKEL SET THEORY ASSERTING THAT SET EQUALITY IS DETERMINED BY THE MEMBERSHIP RELATION

Axiom of extension; Axiom of Extensionality; Axiom extensionality; Extensionality axiom; Axiom of equality

In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of extensionality, or axiom of extension, is one of the axioms of Zermelo–Fraenkel set theory. It says that sets having the same elements are the same set.

https://en.wikipedia.org/wiki/Axiom_of_extensionality

linear map

$The function f:\R^2 \to \R^2 with f(x, y) = (2x, y) is a linear map. This function scales the x component of a vector by the factor 2.$
$The function f(x, y) = (2x, y) is additive: It doesn't matter whether vectors are first added and then mapped or whether they are mapped and finally added: f(\mathbf a + \mathbf b) = f(\mathbf a) + f(\mathbf b)$
$The function f(x, y) = (2x, y) is homogeneous: It doesn't matter whether a vector is first scaled and then mapped or first mapped and then scaled: f(\lambda \mathbf a) = \lambda f(\mathbf a)$

MAPPING THAT PRESERVES THE OPERATIONS OF ADDITION AND SCALAR MULTIPLICATION

Linear operator; Linear mapping; Linear transformations; Linear operators; Linear transform; Linear maps; Linear isomorphism; Linear isomorphic; Linear Transformation; Linear Transformations; Linear Operator; Homogeneous linear transformation; User:The Uber Ninja/X3; Linear transformation; Bijective linear map; Nonlinear operator; Linear Schrödinger Operator; Vector space homomorphism; Vector space isomorphism; Linear extension of a function; Linear extension (linear algebra); Extend by linearity; Linear endomorphism

<mathematics> (Or "linear transformation") A function from a vector space to a vector space which respects the additive and multiplicative structures of the two: that is, for any two vectors, u, v, in the source vector space and any scalar, k, in the field over which it is a vector space, a linear map f satisfies f(u+kv) = f(u) + kf(v). (1996-09-30)

ويكيبيديا

Antisymmetry

In linguistics, antisymmetry is a syntactic theory presented in Richard S. Kayne's 1994 monograph The Antisymmetry of Syntax. It asserts that grammatical hierarchies in natural language follow a universal order, namely specifier-head-complement branching order. The theory is built on the foundation of X-bar theory. Kayne hypothesizes that all phrases whose surface order is not specifier-head-complement have undergone syntactic movements that disrupt this underlying order. Others have posited specifier-complement-head as the basic word order.

Antisymmetry as a principle of word order is reliant on X-bar notions such as specifier and complement, the existence of order-altering mechanisms such as movement, and disputed by constituency structure theories (as opposed to dependency structure theories).

https://en.wikipedia.org/wiki/Antisymmetry