2013/08/27 by Eleftherios Matsikoudis, Edward A. Lee
Computer Science · Mathematics · #Advanced Algebra and Logic #Algebra over a field #Class (philosophy) #Constructive #Fixed Point Theorems Analysis #Function (biology) #Semilattice #Ultrametric space #advanced mathematical theories #cs.LO
paper · pdf · doi:10.4204/eptcs.126.5
published as EPTCS 126, 2013, pp. 56-71 · In Proceedings FICS 2013, arXiv:1308.5896
openalex publication_date 2013/08/27 · arxiv created 2013/09/04 · arxiv updated 2013/09/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
We introduce a new class of abstract structures, which we call generalized ultrametric semilattices, and in which the meet operation of the semilattice coexists with a generalized distance function in a tightly coordinated way. We prove a constructive fixed-point theorem for strictly contracting functions on directed-complete generalized ultrametric semilattices, and introduce a corresponding induction principle. We cite examples of application in the semantics of logic programming and timed computation, where, until now, the only tool available has been the non-constructive fixed-point theorem of Priess-Crampe and Ribenboim for strictly contracting functions on spherically complete generalized ultrametric semilattices.