Logic Workshop

October 27
Arnon Avron, Tel Aviv University
Poincaré-Weyl's predicativity: going beyond $\Gamma_0$

On the basis of Poincaré and Weyl's view of predicativity as invariance, we develop an extensive framework for predicative, type-free first-order set theory in which $\Gamma_0$ and much bigger ordinals can be defined as von Neumann ordinals. This refutes the accepted view of $\Gamma_0$ as the 'limit of predicativity.' We also explain what is wrong in Feferman-Schütte analysis of predicativity on which this view of $\Gamma_0$ is based.