Fixed points and unfounded chains Original Research Article

By an unfounded chain for a function f:X→X we mean a sequence View the MathML source of elements of X s.t. View the MathML source 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.