By an unfounded chain for a function f : X --> X we mean a sequence (x(n))(n is an element of omega) of elements of X s.t. fx(n+1) =x(n) for every n. Unfounded chains can be regarded as a generalization of fixed 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. (C) 2001 Elsevier Science B.V. All rights reserved.

Fixed points and unfounded chains / Bernardi, Claudio. - In: ANNALS OF PURE AND APPLIED LOGIC. - ISSN 0168-0072. - STAMPA. - 109:3(2001), pp. 163-178. [10.1016/s0168-0072(00)00061-0]

Fixed points and unfounded chains

BERNARDI, Claudio
2001

Abstract

By an unfounded chain for a function f : X --> X we mean a sequence (x(n))(n is an element of omega) of elements of X s.t. fx(n+1) =x(n) for every n. Unfounded chains can be regarded as a generalization of fixed 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. (C) 2001 Elsevier Science B.V. All rights reserved.
2001
03b25; 03d45; diagonalizable algebras; fixed points; non-well-founded relations; primary 03f45; secondary 06e25
01 Pubblicazione su rivista::01a Articolo in rivista
Fixed points and unfounded chains / Bernardi, Claudio. - In: ANNALS OF PURE AND APPLIED LOGIC. - ISSN 0168-0072. - STAMPA. - 109:3(2001), pp. 163-178. [10.1016/s0168-0072(00)00061-0]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/34625
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