Let J be any proper ideal of subsets of the real line R which contains all finite subsets of R. We define an ideal J * ∣B as follows: X ∈ J * ∣B if there exists a Borel set $B \subset R \times R$ such that $X \subset B$ and for any x ∈ R we have $\{y \in R: \langle x,y\rangle \in B\} \in \mathscr{J}$ . We show that there exists a family $\mathscr{A} \subset \mathscr{J}^\ast\mid\mathscr{B}$ of power ω (...) 1 such that $\bigcup\mathscr{A} \not\in \mathscr{J}^\ast\mid\mathscr{B}$ . In the last section we investigate properties of ideals of Lebesgue measure zero sets and meager sets in Cohen extensions of models of set theory. (shrink)

We prove that if f is a partial Borel function from one Polish space to another, then either f can be decomposed into countably many partial continuous functions, or else f contains the countable infinite power of a bijection that maps a convergent sequence together with its limit onto a discrete space. This is a generalization of a dichotomy discovered by Solecki for Baire class 1 functions. As an application, we provide a characterization of functions which are countable unions of (...) continuous functions with domains of type Πn0, for a fixed n<ω. For Baire class 1 functions, this generalizes analogous characterizations proved by Jayne and Rogers for n=1 and Semmes for n=2. (shrink)

An explanation is given of why, after adding to a model M of ZFC first a Solovay real r and next a Cohen real c, in M[ r][ c] a Cohen real over M[ c] is produced. It is also shown that a Solovay algebra iterated with a Cohen algebra can be embedded into a Cohen algebra iterated with a Solovay algebra.

We discuss in the paper the following problem: Given a function in a given Baire class, into "how many" (in terms of cardinal numbers) functions of lower classes can it be decomposed? The decomposition is understood here in the sense of the set-theoretical union.

Any finite support iteration of posets with precalibre ℵ 1 which has the length of cofinality greater than ω 1 yields a model for the dual Borel conjecture in which the real line is covered by ℵ 1 strong measure zero sets.

We study the degree of (weak) Q-pointness, and that of (weak) P-pointness, of ideals on a regular infinite cardinal.

We introduce a new cardinal characteristic r*, related to the reaping number r, and show that posets of size $ r* which add reals add unbounded reals; posets of size $ r which add unbounded reals add Cohen reals. We also show that add(M) ≤ min(r, r*). It follows that posets of size < add(M) which add reals add Cohen reals. This improves results of Roslanowski and Shelah [RS] and of Zapletal [Z].

The prohibition of commercialisation of the human body and its parts is not applied consistently and suffers from many exceptions in the human biological material (HBM) market. Examples include the possibility of patenting certain HBM-derived products and their commercial marketing or payments for blood donations. Thus, the current practice of marketing HBM-derived products makes the altruistic donor most vulnerable to exploitation while being deprived of benefits. There seem to be two ways to improve this state of affairs. The first is (...) to apply consistently the prohibition of commercialisation of the body and its parts to commercially marketed tissue and cell products as well. This would require limiting the possibility of financial gain associated with the processing, distribution and sale of HBM-based products. Such a solution, however, does not seem to gain wide acceptance or have a chance of implementation in the near future. Therefore, introducing more transparent rules and greater donor empowerment seems more reasonable by exempting HBM from the ban on commercialisation under certain conditions and with clear limitations. (shrink)

We show that for an uncountable κ in a suitable Cohen real model for any family {A ν } ν<κ of sets of reals there is a σ-homomorphism h from the σ-algebra generated by Borel sets and the sets A ν into the algebra of Baire subsets of 2 κ modulo meager sets such that for all Borel B, B is meager iff h(B) = 0. The proof is uniform, works also for random reals and the Lebesgue measure, and in (...) this way generalizes previous results of Carlson and Solovay for the Lebesgue measure and of Kamburelis and Zakrzewski for the Baire property. (shrink)

Let P be any one of the following combinatorial properties: weak P-pointness, weak (semi-) Q-pointness, weak (semi-)selectivity, ω-closedness. We deal with the following two questions: (1) What is the least cardinal κ such that there exists an ideal with κ many generators that does not have the property P? (2) Can one extend every ideal with the property P to a prime ideal with the property P?

We construct a G δ set G ⊆ ω ω ×2 ω with null vertical sections such that each perfect set P ⊆2 ω meets almost all vertical sections of G in the following sense: we can define from P subsets S of ω of density zero such that whenever the section determined by x ∈ ω ω does not meet P , then x ∈ S for all but finitely many i . This generalizes theorems of Mokobodzki and Brendle (...) et al. 185–199). (shrink)

The development of research based on human biological material has contributed to a lively debate on the concept of informed consent in these studies, particularly its scope, form and length of validity. The biggest disputes and doubts concern the range of consent for research that will be conducted in the future, whose aim and place are unknown at the time of the sample collection, as are the future researchers and the ability to use the previously collected materials again. This situation (...) raises the question of a just and prudent balance between the rights of participants in the research and the rights of researchers. New forms of consent have been proposed, which sometimes substantially diverge from the classical model in aiming towards responsible balancing between the necessity to protect the donors’ interests and the possibility of conducting research in medicine. These new concepts also find their application in legislative acts adopted internationally and in some European countries in the recent years. (shrink)

We prove that if the Mathias forcing is followed by a forcing with the Laver Property, then any V\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {V}$$\end{document}-q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {q}$$\end{document}-point is isomorphic via a ground model bijection to the canonical V\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {V}$$\end{document}-Ramsey ultrafilter added by the Mathias real. This improves a result of Shelah and Spinas.

Biobanki populacyjne stwarzają nowe możliwości prowadzenia badań biomedycznych oraz rozwoju medycyny personalizowanej i genomiki zdrowia publicznego. Z drugiej strony niosą wyzwania w zakresie zagwarantowania praw dawców (świadoma zgoda, zachowanie prywatności i poufności, niedyskryminacja w oparciu o dziedzictwo genetyczne). Główne wymiary, w których realizować się może ochrona praw dawców, to: właściwa komunikacja zarówno na poziomie społecznym (konsultacje społeczne) jak i indywidualnym (proces uzyskiwania świadomej zgody od dawców), odpowiednia organizacja biobanku (bezpieczny system informatyczny, kodowanie i anonimizacja danych, reguły dostępu do danych), właściwy (...) nadzór nad działalnością biobanku (zazwyczaj sprawowany przez komisję etyczną i komitet naukowy), a także stworzenie odpowiednich regulacji prawnych dotyczących pobierania, przechowywania i udostępniania ludzkiego materiału biologicznego oraz zapobiegających dyskryminacji ze względu na dziedzictwo genetyczne. W artykule opisane zostały również zasady organizacji i funkcjonowania biobanków populacyjnych w wybranych krajach europejskich (Estonia, Hiszpania, Wielka Brytania) w kontekście respektowania praw dawców. (shrink)

The Covering Property Axiom, which attempts to capture some of the combinatorics of the Sacks model, the model obtained from by countable support iteration of length of the Sacks forcing, seems to miss a Suslin tree. We add a diamond polish to the axiom to remedy this.

The authors investigate an operation * on the subsets of ${\mathcal{P}(\mathbb{R})}$ . It is connected with Borel’s strong measure zero sets as well as strongly meager. The results concern the behaviour of the family of countable sets when * is applied.