arXiv subjects
Publications and source records attributed to V. M. Zhuravlov.
The article proposes a method for constructing non-standard theories based on terms from partially existing sequences of elements. The method is illustrated by the example of the theory of monoids. Predicates and terms from non-standard sequences, 2023, udc: 510.65 msc: 03H05 Key words: monoid, term, ideal, category, isomorphizm, insignificant extension of the theory, non-standard theory
The article introduces the concept of uniformity, which is formulated as a scheme of axioms. The connection of this concept with ordered sets is studied. The effectiveness of using axiom schemes as a convenient and short way of replacing axiom systems is shown. With such a replacement, the main idea of the system of axioms of the given mathematical theory immediately becomes clear. The reasons for using number systems in mathematics are also shown.