 The basic axioms and rules of inference governing statements in our second-order language are similar to those of the first-order predicate calculus with identity, though they’ve been extended to apply to claims involving universal quantifiers binding relation variables. Where \(\phi\), \(\psi\), and \(\chi\) are any formulas, \(\alpha\) any variable and \(\tau\) any term of the same type as \(\alpha\) (i.e., both are object terms or both are \(n\)-place relation terms), then the following are the basic axioms and rules of second-order logic: 