 \(T_{{o}}\) denotes truth. The meaning of \(\Pi_{{o}({o}\alpha)}\) was discussed in  Section 1.1.  To see that this definition of \(\Pi_{{o}({o}\alpha)}\) is appropriate, note that \(\lambda x_{\alpha}T\) denotes the set of all elements of type α, and that \(\Pi_{{o}({o}\alpha)}s_{{o}\alpha}\) stands for \(\sfQ_{{o}({o}\alpha)({o}\alpha)}[\lambda x_{\alpha}T] s_{{o}\alpha}\), respectively for \([\lambda x_{\alpha}T] = s_{{o}\alpha}\). Therefore \(\Pi_{{o}({o}\alpha)}s_{{o}\alpha}\) asserts that \(s_{{o}\alpha}\) is the set of all elements of type α, so \(s_{{o}\alpha}\) contains all elements of type α. It can be seen that \(F_{{o}}\) can also be written as \(\forall x_{{o}}x_{{o}}\), which asserts that everything is true. This is false, so \(F_{{o}}\) denotes falsehood. The expression \(\lambda g_{{o}{o}{o}}[g_{{o}{o}{o}}x_{{o}}y_{{o}}]\) can be used to represent the ordered pair \(\langle x_{{o}},y_{{o}}\rangle\), and the conjunction \(x_{{o}} \land y_{{o}}\) is true iff \(x_{{o}}\) and \(y_{{o}}\) are both true, i.e., iff \(\langle T_{{o}},T_{{o}}\rangle = \langle x_{{o}},y_{{o}}\rangle\). Hence \(x_{{o}} \land y_{{o}}\) can be expressed by the formula \([\lambda g_{{o}{o}{o}}[g_{{o}{o}{o}}T_{{o}}T_{{o}}]] = [\lambda g_{{o}{o}{o}}[g_{{o}{o}{o}}x_{{o}}y_{{o}}]]\).