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 -

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

**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 -

... A relation R is said to be

**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

... 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 ...

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