Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 40, Number 2 (1999), 197-205.
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.
Notre Dame J. Formal Logic, Volume 40, Number 2 (1999), 197-205.
First available in Project Euclid: 3 December 2002
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Esser, Olivier; Hinnion, Roland. Antifoundation and Transitive Closure in the System of Zermelo. Notre Dame J. Formal Logic 40 (1999), no. 2, 197--205. doi:10.1305/ndjfl/1038949536. https://projecteuclid.org/euclid.ndjfl/1038949536