We prove: Theorem 1. Let Îº be an uncountable cardinal. Every Îº-Suslin graph G on reals satisfies one of the following two requirements: (I) G admits a (Îº+ 1)-Borel colouring by ordinals below Îº; (II)â€¦ (More)

Wedemonstrate that a comprehensive nonstandard set theory can be developed in the standard âˆˆ-language. As an illustration, a nonstandard Law of Large Numbers is obtained.

We prove that orbit equivalence relations (ERs, for brevity) of generically turbulent Polish actions are not Borel reducible to ERs of a family which includes Polish actions of Sâˆž, the group of allâ€¦ (More)

The aim of this paper is to demonstrate that several nonâ€“rigorous methods of mathematical reasoning in the field of divergent series, mostly related to the Euler and Hutton transforms, may beâ€¦ (More)

T he theories as developed by European mathematicians prior to 1870 differed from the modern ones in that none of them used the modern theory of limits. Fermat develops what is sometimes called aâ€¦ (More)

The ABCs of the History of Infinitesimal Mathematics The ABCs of the history of infinitesimal mathematics are in need of clarification. To what extent does the famous dictum â€œhistory is alwaysâ€¦ (More)