A stable formula in model theory is a first-order formula 
without the order property. Explicitly, there must be no model with infinite sequences
and 
such that 
holds iff 
. By compactness, this is equivalent to a finite bound
on the lengths of such patterns.
A theory is stable when all its formulas are stable. For example, equality cannot encode arbitrarily long strict order patterns, whereas
the formula 
in a dense linear order can. The stable forking
conjecture asks whether this well-behaved kind of formula always suffices to
witness forking in the wider class of simple
theories.
