 Here \(\p_i(\xbar_i,\ybar)\) is a formula with at most the free variables shown, \(\abar\) is a sequence of elements of M corresponding to \(\ybar\), and \(\p_i(\xbar_i,\abar)^{\M,\xbar_i}\) is the extension of \(\p_i(\xbar_i,\ybar)\) in \(\M\) relative to \(\abar\), i.e., the set of \(n_i\)-tuples \(\bbar_i\) such that \(\M\models\p_i(\bbar_i,\abar)\).