 ##  [Definable Set](/definable-set) 

  ##  [Definable Set](https://mathlogic.quantumdictionary.io/definable-set-0) 

  
 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

A subset S of the domain of a structure M is definable (with parameters) if there exists a first-order formula φ(x, a) with parameters a from M such that S = { b in M : M ⊨ φ(b,a)}. If no parameters are used the set is definable without parameters (0‑definable).

 
 ##  [Definable Set](https://algebra.quantumdictionary.io/definable-set-1) 

  
 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 
Definition

A definable set in a structure M is a subset of M^n that equals the solution set of a first-order formula φ(x) possibly with parameters from M; that is, D = { a ∈ M^n : M ⊨ φ(a) } for some φ and parameter tuple from M.