On Some Model Theoretic Properties of Totally Bounded Ultrametric Spaces

Gábor Sági and Karrar Al-Sabti
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Gábor Sági: Alfréd Rényi Institute of Mathematics, P.O. Box 127, H-1364 Budapest, Hungary
Karrar Al-Sabti: Faculty of Computer Science and Mathematics, University of Kufa, P.O. Box 21, Kufa 540011, Najaf, Iraq

Mathematics, 2022, vol. 10, issue 12, 1-9

Abstract: Continuing investigations initiated by the first author, we associate relational structures for metric spaces and investigate their model theoretic properties. In this paper, we consider ultrametric spaces. Among others, we show that any elementary substructure of the relational structure associated with a totally bounded ultrametric space X is dense in X . Further, we provide an explicit upper bound for a splitting chain of atomic types in ultrametric spaces of a finite spectrum. For ultrametric spaces, these results improve previous ones of the present authors and may have further practical applications in designing similarity detecting algorithms.

Keywords: model theoretic stability; ultrametric spaces; totally bounded spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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