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PREUVES, PROGRAMMES et SYSTÈMES |  |
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PREUVES, PROGRAMMES et SYSTÈMES | |
| HAL : hal-00150886, version 1 |
| Fiche détaillée |  Récupérer au format |
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| TYPES'04, Jouy-en-Josas : France (2006) |
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| Lambda-Z: Zermelo's Set Theory as a PTS with 4 Sorts |
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| Alexandre Miquel 1 |
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| (2006) |
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| We introduce a pure type system (PTS) lambda-Z with four sorts and show that this PTS captures the proof-theoretic strength of Zermelo's set theory. For that, we show that the embedding of the language of set theory into Lambda-Z via the `sets as pointed graphs' translation makes lambda-Z a conservative extension of IZ+AFA+TC (intuitionistic Zermelo's set theory plus Aczel's antifoundation axiom plus the axiom of transitive closure) - a theory which is equiconsistent to Zermelo's. The proof of conservativity is achieved by defining a retraction from lambda-Z to a (skolemised version of) Zermelo's set theory and by showing that both transformations commute via the axioms AFA and TC. |
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| 1 : | Preuves, Programmes et Systèmes (PPS) |
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CNRS : UMR7126 – Université Paris VII - Paris Diderot |
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| Domaine | : | Informatique/Logique en informatique |
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| Lambda calculus – Pure type systems – Set theory |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00150886, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00150886 | |
| oai:hal.archives-ouvertes.fr:hal-00150886 | |
| Contributeur : Alexandre Miquel | |
| Soumis le : Dimanche 3 Juin 2007, 22:26:15 | |
| Dernière modification le : Mardi 12 Juin 2007, 15:07:53 | |
