This article demonstrates the use of axiom schemes to improve the representation of ordered numerical systems, suggesting enhanced logical tools.
The paper studies methods of axiomatizing linearly ordered sets that use axiom schemes. This allows one to shorten the axiomatics and better reveal the general meaning of order. It is shown that axiom schemes are a powerful, and possibly underestimated, logical tool. Schemes are proposed for the ordered numerical systems— N, Z, Q, R. Thus, by sometimes introducing certain constants into consideration, we obtain algebraizations of these order-theoretic and topological models. The article is written in English, but the ZIP appendix contains a Ukrainian-language version. "Axiom schemes for linearly ordered numerical systems", udc: 510.65 msc: 03B16, Volodymyr M. Zhuravlov,
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Volodymyr M. Zhuravlov (2026) studied this question.