Definition 4: Given statements \phi and \psi , we refer to the statement “ \phi and \psi ” as the conjunction of \phi and \psi . To express this, we may also use notation like (\phi \wedge \psi). Moreover, we may use the following recursively defined notation:
(a) Base cases: We understand (\alpha \wedge \beta \wedge \gamma) to mean \big( (\alpha \wedge \beta) \wedge \gamma \big) .
(b) Recursion: If (\alpha \wedge \beta \wedge \cdots \wedge \psi) is understood, then we may further use the abbreviation (\alpha \wedge \beta \wedge \cdots \wedge \psi \wedge \omega) \hspace{3mm} \textup{for} \hspace{3mm} \big( (\alpha \wedge \beta \wedge \cdots \wedge \psi) \wedge \omega \big).
A statement of this form may be referred to as a generalized conjunction.