Antonius J. C. Hurkens

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We study logical systems for reasoning about equations involving recursive deenitions. In particular, we are interested in propositionall fragments of the functional language of recursion FLR 18, 17], i.e., without the value passing or abstraction allowed in FLR. The pure, propositional fragment FLR0 turns out to coincide with the iteration theories of 1].(More)
The axioms of set theory are sometimes motivated as follows: (1) A collection is a set ii at some stage all of its members exist. (2) A set exists at some stage ii at some earlier stage all of its members exist. In order to justify the Axiom of Foundation, one often adds: (3) The stages are well-ordered by \earlier than". This is a circular \reduction" of(More)
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