A minimal predicative set theory
The authors choose a very weak set theory, denoted by N, having just the following axioms: (1) \(\emptyset\) exists, and (2) for any two sets \(x\), \(y\), \(x\cup \{y\}\) exists, and prove that Robinson's arithmetic Q is interpretable in N. This is to be understood as a reasonable reduction from the point of view of Hilbert's Program, which continues analogous work of E. Nelson. The proof of the interpretability of Q into N is given through a large number of steps which are a bit difficult to follow. A finistic proof of Herbrand consistency of N is also given.
scientific article; zbMATH DE number 721964