 ##  [Arithmetical Hierarchy](/index.php/arithmetical-hierarchy) 

  ##  [Arithmetical Hierarchy](https://mathlogic.quantumdictionary.io/arithmetical-hierarchy-0) 

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

- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

A stratification of predicates and formulas about natural numbers by the pattern and number of alternating first-order quantifiers; classes are usually denoted Σ_n, Π_n and Δ_n and classify definability and decidability in first-order arithmetic.