2023 Volume 34 Issue 2 Pages 43-50
The present paper proposes principles to arrange linearly species and groups of species according to the lexicographic order based on the framework that Yamaguchi and Shiono (2022) proposed for mathematical formulation of basic concepts of biostratigraphy. Under the assumption that a set of species S and time ranges of all species in S are given, the following results are obtained: i) all elements of S are comparative under the relation ⊰ defined according to the lexicographic order of time ranges, and therefore S is a totally ordered set, ⅱ) all subsets of S are comparative under the relation ≼ defined according to the lexicographic order based on the relation ⊰ on S, and therefore the power set of S is a totally ordered set, ⅲ) If a set S satisfies a condition H, then the relation ≼ between two sets of species existing at the same time corresponds to the chronological order, and ⅳ) the order relation ≪ between two short time intervals defined by the time ranges of species also corresponds to the order relation ≼ between sets of species that existed at corresponding intervals. It is expected that the results contribute to the formalization of mathematical bases of biostratigraphy.
