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Remark 15

[2DC]It is assumed as an axiom that

\begin{equation} \label{eq:forall_ exists} ¬ (∀ x, 𝜙 ) ⇔ (∃ x, ¬ 𝜙 ) ~ ~ . \end{equation}

(In Sec. 2.1 in [ 10 ] indeed \((∀ x, 𝜙)\) is presented as short form for \(¬(∃ x, ¬𝜙)\)).

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Authors: "Mennucci , Andrea C. G." .

Bibliography

[15] P.G. Hinman. Fundamentals of Mathematical Logic. Taylor & Francis, 2005. ISBN 9781568812625. URL https://books.google.it/books?id=xA6D8o72qAgC.

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