##  [Complete Type](/complete-type) 

  ##  [Complete Type](https://mathlogic.quantumdictionary.io/complete-type-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 & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A complete type (also called a complete n-type) is a maximal consistent set of first-order formulas with parameters in a given structure or over a parameter set, in a fixed tuple of free variables; it assigns, for every formula in those variables, either the formula or its negation, thereby describing all first-order properties that a tuple can satisfy relative to the parameter set.

 

 

 

 

 





 

 



 ##  [Complete Type](https://algebra.quantumdictionary.io/complete-type-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 complete type over a parameter set A is a maximal consistent set of first-order formulas with parameters from A: for every formula φ(x,a) with parameters a from A, the type contains either φ(x,a) or its negation, and the whole set remains consistent with the theory T.