Antifoundation and transitive closure in the system of zermelo

The role of foundation with respect to transitive closure in the Zermelo system Z has been investigated by Boffa; our aim is to explore the role of antifoundation. We start by showing the consistency of “Z + antifoundation + transitive closure” relative to Z (by a technique well known for ZF). Further, we introduce a “weak replacement principle” (deductible from antifoundation and transitive closure) and study the relations among these three statements in Z via interpretations. Finally, we give some adaptations for ZF without infinity. © 1999 by the University of Notre Dame. All rights reserved.SCOPUS: ar.jinfo:eu-repo/semantics/publishe