A New Approach to Predicative Set Theory

We suggest a new framework for the Weyl-Feferman predicativist program by constructing a formal predicative set theory P ZF which resembles ZF , and is suitable for mechanization. The basic idea is that the predicatively acceptable instances of the comprehension schema are those which determine the collections they define in an absolute way, independent of the extension of the “surrounding universe”. The language of P ZF is type-free, and it reflects real mathematical practice in making an extensive use of statically defined abstract set terms. Another important feature of P ZF is that its underlying logic is ancestral logic (i.e. the extension of first-order logic with a transitive closure operation)
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