 ##  [Omega-Consistency](/index.php/omega-consistency) 

  ##  [Omega-Consistency](https://mathlogic.quantumdictionary.io/omega-consistency-0) 

  
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- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

A strengthening of syntactic consistency for formal theories in arithmetic: a theory T is omega-consistent if there is no formula φ(x) such that T proves every numeral instance φ(0), φ(1), φ(2), ... and simultaneously T proves ∃x ¬φ(x) (equivalently T proves ¬∀x φ(x)).