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On computing the transitive closure of a relation

✍ Scribed by J. Eve; R. Kurki-Suonio

Publisher: Springer-Verlag
Year: 1977
Tongue: English
Weight: 647 KB
Volume: 8
Category: Article
ISSN: 0001-5903
DOI: 10.1007/bf00271339

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## Abstract We will prove in Zermelo‐Fraenkel set theory __without axiom of choice__ that the transitive hull __R__\* of a relation __R__ is not much “bigger” than __R__ itself. As a measure for the size of a relation we introduce the notion of κ^+^‐__narrowness__ using __surjective__ Hartogs numbe