A Connection between Leibniz’ Infinitely Small Quantities and the Analytical Hierarchy

摘要: In this paper I want to show among other things one unexpected connection between the usage of infinitely small quantities and analytical hierarchy sets. The is due Leibniz but use modern version by working in a theory similar Nelson’s Internal set theory1. weaker than think that it contains minimum for reasonable work with quantities. Hence results can be applied large amount structures my opinion more original infinitesimals e.g. just mentioned. A part technique which was developed alternative theory2 hence mention also some ideas concerning theory. This also, opinion, accordance main themes conference. Using our we find an exact, even algorithmical notions defined help corresponding definable Cantor’s deals actual infinity used as basis mathematics. spite method exact translations, translations are comprehensible only case classical such limit, continuity, limit point etc. For complicated (some them will specified later) obtain known algorithms incomprehensible give argument why situation takes place. It interesting translation algorithm introduced me complexity nonstandard definition has its counterpart standard translation. concept mentioned concerns sets talk about.