A note of provability, truth and existence
The paper shows that if \(T\) is any consistent extension of Peano Arithmetic, there is a false \(\Sigma_ 1\) formula, \(A\), and a true \(\Pi_ 1\) formula, \(B\), such that \(T\cup \{ A\}\) is consistent, \(T\not\vdash B\), but \(T\cup \{ A\}\vdash B\). It also shows that \(B\) may be of the form Con(\(S\)) where \(S\) is a consistent theory. It cites these results as supporting the critique of Gödel's philosophy of mathematics by \textit{S. Feferman} [``Infinity in mathematics: Is Cantor necessary'', in: (\textit{G. Tolrado di Francia} (ed.)) Infinity in science, Inst. Enciclopedia Italiana, Rome (1987)].
scientific article; zbMATH DE number 28339