The independence property for a formula 
in a theory 
is the condition that, for every positive
integer 
,
there are tuples of parameters 
such that, for every subset 
, some tuple 
satisfies 
exactly when 
. Thus 
can encode every collection of the 
parameters.
A theory has the independence property if one of its formulas does. A theory with no such formula is called NIP, short for "not the independence property." NIP is a central tameness condition in model theory and is closely related to finite Vapnik-Chervonenkis dimension.
