FLORENSKY’S PHILOSOPHICAL IDEAS AND THE THEORY OF SETS OF CANTOR

The article considers the role of the idea of actual infinity in the works of Florensky. The introduction briefly traces the history of ideas about the actual infinity in European culture to the works of George Cantor. The reaction of European scientists and religious figures to the emergence of the “naïve” theory of Cantor sets is characterized. A detailed analysis of the connection between Florensky and George Cantor’s ideas is given. Many quotations from the 1904 work on the symbols of Infinity are given, which illustrate the influence of Cantor’s works on Florensky. The presentation of Florensky’s religious and philosophical ideas of Cantor about the actual infinity is given. Emphasized understanding Florensky transfinite numbers Cantor as symbols.

Applying Set Theory E88

We prove some results in set theory as applied to general topology and model theory. In particular, we study ℵ1-collectionwise Hausdorff, Chang Conjecture for logics with Malitz-Magidor quantifiers and monadic logic of the real line by odd/even Cantor sets.

The Family of Central Cantor Sets with Packing Dimension Zero

As in the recent article of M. Balcerzak, T. Filipczak and P. Nowakowski, we identify the family CS of central Cantor subsets of [0, 1] with the Polish space X : = (0, 1)ℕ equipped with the probability product measure µ. We investigate the size of the family P 0 of sets in CS with packing dimension zero. We show that P 0 is meager and of µ measure zero while it is treated as the corresponding subset of X. We also check possible inclusions between P 0 and other subfamilies CS consisting of small sets.

Uniformization of Cantor sets with bounded geometry

In this note we provide a quasisymmetric taming of uniformly perfect and uniformly disconnected sets that generalizes a result of MacManus [Rev. Mat. Iberoamericana 15 (1999), pp. 267–277] from 2 to higher dimensions. In particular, we show that a compact subset of R n \mathbb {R}^n is uniformly perfect and uniformly disconnected if and only if it is ambiently quasiconformal to the standard Cantor set C \mathcal {C} in R n + 1 \mathbb {R}^{n+1} .

Theoretical fractional formulation of a three-dimensional radio frequency ion trap (Paul-trap) for optimum mass separation

We investigate the dynamics of an ion confined in a Paul–trap supplied by a fractional periodic impulsional potential. The Cantor–type cylindrical coordinate method is a powerful tool to convert differential equations on Cantor sets from cantorian–coordinate systems to Cantor–type cylindrical coordinate systems. By applying this method to the classical Laplace equation, a fractional Laplace equation in the Cantor–type cylindrical coordinate is obtained. The fractional Laplace equation is solved in the Cantor–type cylindrical coordinate, then the ions is modelled and studied for confined ions inside a Paul–trap characterized by a fractional potential. In addition, the effect of the fractional parameter on the stability regions, ion trajectories, phase space, maximum trapping voltage, spacing between two signals and fractional resolution is investigated and discussed.