Generalized Silver and Miller measurability

Silver Measurability and Its Relation to Other Regularity Properties

For a ⊆ b ⊆ ω with b\a infinite, the set D = {x ∈ [ω] : a ⊆ x ⊆ b} is called a doughnut. Doughnuts are equivalent to conditions of Silver forcing, and so, a set S ⊆ [ω] is called Silver measurable, also known as completely doughnut, if for every doughnut D there is a doughnut D′ ⊆ D which is contained or disjoint from S. In this paper, we investigate the Silver measurability of ∆2 and Σ 1 2 set...

On the separation of regularity properties of the reals

We present a model where ω1 is inaccessible by reals, Silver measurability holds for all sets but Miller and Lebesgue measurability fail for some sets. This contributes to a line of research started by Shelah in the 1980s and more recently continued by Schrittesser and Friedman (see [7]), regarding the separation of different notions of regularity properties of the real line. Acknowledgement. T...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

On Generalized Step-functions and Superposition Operators

For a given σ-ideal of sets, the notion of a generalized stepfunction is introduced and investigated in connection with the problem of sup-measurability of certain functions of two variables, regarded as superposition operators. 2000 Mathematics Subject Classification: 28A05, 28D05.

Set Theory, Forcing and Real Line

We give a very brief survey on ZFC theory (Zermelo-Fraenkel Set Theory) and we present an intuitive introduction to the method of forcing and some applications to the real line. Our exposition will be very informal, without any claim of completeness and rigour. The idea is just to give a very intuitive idea of what Set Theory and forcing-method are, and why they are interesting and useful from ...