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 the notation (\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 an iterated conjunction, or just a conjunction if the context is clear. We express (\alpha \wedge \beta \wedge \cdots \wedge \omega) in natural language as “ \alpha and \beta and \cdots and \omega “, or similar.