✦ LIBER ✦

Fixed points and unfounded chains

✍ Scribed by Claudio Bernardi

Book ID: 104307094
Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 143 KB
Volume: 109
Category: Article
ISSN: 0168-0072
DOI: 10.1016/s0168-0072(00)00061-0

No coin nor oath required. For personal study only.

✦ Synopsis

By an unfounded chain for a function f : X → X we mean a sequence (xn)n∈! of elements of X s.t. fxn+1 = xn for every n. Unfounded chains can be regarded as a generalization of ÿxed points, but on the other hand are linked with concepts concerning non-well-founded situations, as ungrounded sentences and the hypergame. In this paper, among other things, we prove a lemma in general topology, we exhibit an extensional recursive function from the set of sentences of PA into itself without an unfounded chain, and we prove that every term in a Magari algebra (or diagonalizable algebra) has an unfounded chain.

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