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Definable relations

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Definable relations

Definable relations - раздел Математика, A set in mathematics is a collection of well defined and distinct objects, considered as an object in its own right An N-Ary Relation R On The Universe M Of A Structure ...

An n-ary relation R on the universe M of a structure is said to be definable (or explicitly definable, or -definable) if there is a formula φ(x₁,...,x_n) such that

In other words, R is definable if and only if there is a formula φ such that

is correct.

An important special case is the definability of specific elements. An element m of M is definable in if and only if there is a formula φ(x) such that

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A set in mathematics is a collection of well defined and distinct objects, considered as an object in its own right

A is a proper subset of B and conversely B is a proper superset of A... In set theory and related branches of mathematics a collection F of subsets... If every member of set A is also a member of set B then A is said to be a subset of B written A B A is...

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Non-injective and surjective
· ·

Definable relations
An n-ary relation R on the universe M of a structure is said to be defin

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Definitions
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