 ##  [Alternation Depth](/alternation-depth) 

  ##  [Alternation Depth](https://mathlogic.quantumdictionary.io/alternation-depth-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

The number of alternations between existential and universal quantifiers in the longest alternating sequence of a formula; equivalently, the count of switches from ∃ to ∀ or ∀ to ∃ along a maximal path through quantifier occurrences.