2010/05/11 by Yuri A. Rylov, Rylov, Yuri A.
Engineering · Mathematics · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #FOS: Mathematics #General Mathematics (math.GM) #History and Theory of Mathematics #Mathematics and Applications #math.GM
paper · pdf · doi:10.48550/arxiv.1005.2074
15 pages, 0 figures, correction of misprints
openalex publication_date 2010/05/11 · arxiv created 2010/05/19 · arxiv updated 2010/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Properties of the logical reloading in the Euclidean geometry are considered. The logical reloading is a logical operation which replaces one system of basic concepts of a conception by another system of basic concepts of the same conception. The logical reloading does not change propositions of the conception. However, generalizations of the conception are different for different systems of basic concepts. It is conditioned by the fact, that some systems of basic concepts contain not only propositions of the conception, but also some attributes of this conception description. Properties of the logical reloading are demonstrated in the example of the proper Euclidean geometry, whose generalization leads to different results for different system of basic concepts.