2014/12/23 by Frédéric Blanqui, Blanqui, Frédéric
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topology and Set Theory #FOS: Computer and information sciences #FOS: Mathematics #Functional Equations Stability Results #Logic (math.LO) #Logic in Computer Science (cs.LO) #cs.LO #math.LO
paper · pdf · doi:10.48550/arxiv.1502.06021
arxiv created 2014/12/23 · openalex publication_date 2014/12/23 · arxiv updated 2015/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (X,≤) be a \em non-empty strictly inductive poset, that is, a non-empty partially ordered set such that every non-empty chain Y has a least upper bound lub(Y)∈ X, a chain being a subset of X totally ordered by ≤. We are interested in sufficient conditions such that, given an element a0∈ X and a function f:X\a X, there is some ordinal k such that ak+1=ak, where a_k is the transfinite sequence of iterates of f starting from a0 (implying that ak is a fixpoint of f): \beginitemize\itemsep=0mm \item ak+1=f(ak) \item al=\lub\ak| k \textless l\ if l is a limit ordinal, i.e. l=lub(l) \enditemize This note summarizes known results about this problem and provides a slight generalization of some of them.