Definable

In mathematical logic, the word definable may refer to:

  • A definable real number.
  • A definable set.
  • A definable integer sequence.
  • A definable function
  • A relation or function definable over a first order structure.
  • A mathematical object or concept that is well-defined.

Other articles related to "definable":

Structure (mathematical Logic) - Structures and First-order Logic - Definable Relations
... 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...xn) such that In ... An element m of M is definable in if and only if there is a formula φ(x) such that ...
Structure (mathematical Logic) - Structures and First-order Logic - Definable Relations - Definability With Parameters
... A relation R is said to be definable with parameters (or -definable) if there is a formula φ with parameters from such that R is definable using φ ... Every element of a structure is definable using the element itself as a parameter ...
Beth Definability - Statement
... Less formally a property is implicitly definable in a theory in language L (via introduction of a new symbol φ of an extended language L') only if that property is explicitly definable in that theory (by ... That is, a "property" is implicitly definable with respect to a theory if and only if it is explicitly definable ...
Definable Set - Invariance Under Automorphisms
... An important result about definable sets is that they are preserved under automorphisms ... Let be an -structure with domain, and definable in with parameters from ... all , if and only if This result can sometimes be used to classify the definable subsets of a given structure ...