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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
