We consider several kinds of partition relations on the set ${\mathbb{R}}$ of real numbers and its powers, as well as their parameterizations with the set ${[\mathbb{N}]^{\mathbb{N}}}$ of all infinite sets of natural numbers, and show that they hold in some models of set theory. The proofs use generic absoluteness, that is, absoluteness under the required forcing extensions. We show that Solovay models are absolute under those forcing extensions, which yields, for instance, that in these models for every well ordered partition (...) of ${\mathbb{R}^\mathbb{N}}$ there is a sequence of perfect sets whose product lies in one piece of the partition. Moreover, for every finite partition of ${[\mathbb{N}]^{\mathbb{N}} \times \mathbb{R}^{\mathbb{N}}}$ there is ${X \in [\mathbb{N}]^{\mathbb{N}}}$ and a sequence ${\{P_{k} : k \in \mathbb{N}\}}$ of perfect sets such that the product ${[X]^{\mathbb{N}} \times \prod_{k}^{\infty}P_{k}}$ lies in one piece of the partition, where ${[X]^{\mathbb{N}}}$ is the set of all infinite subsets of X. The proofs yield the same results for Borel partitions in ZFC, and for more complex partitions in any model satisfying a certain degree of generic absoluteness. (shrink)

Given a topological Ramsey space math formula, we extend the notion of semiselective coideal to sets math formula and study conditions for math formula that will enable us to make the structure math formula a Ramsey space and also study forcing notions related to math formula which will satisfy abstract versions of interesting properties of the corresponding forcing notions in the realm of Ellentuck's space. This extends results from to the most general context of topological Ramsey spaces. As applications, we (...) prove that for every topological Ramsey space math formula, under suitable large cardinal hypotheses every semiselective ultrafilter math formula is generic over math formula; and that given a semiselective coideal math formula, every definable subset of math formula is math formula-Ramsey. This generalizes the corresponding results for the case when math formula is equal to Ellentuck's space. (shrink)

Several types of polarized partition relations are considered. In particular we deal with partitions defined on cartesian products of more than two factors. MSC: 03E05.

The Continuum Hypothesis has motivated a considerable part of the development of axiomatic set theory for over a century. We present, in a very schematic way, some of the results that give information related to Cantor’s Continuum Problem.

We prove that the least σ-algebra containing the projective sets and closed under projections is exactly the collection of hyperprojective sets which, with their complements, can be inductively defined with real parameters by an induction of countable length. This provides a construction principle for this natural class of hyperprojective sets.

The Principle of Ariadne, formulated in 1988 ago by Walter Carnielli and Carlos Di Prisco and later published in 1993, is an infinitary principle that is independent of the Axiom of Choice in ZF, although it can be consistently added to the remaining ZF axioms. The present paper surveys, and motivates, the foundational importance of the Principle of Ariadne and proposes the Ariadne Game, showing that the Principle of Ariadne, corresponds precisely to a winning strategy for the Ariadne Game. (...) Some relations to other alternative. set-theoretical principles are also briefly discussed. (shrink)

We study several perfect set properties of the Baire space which follow from the Ramsey property ω→(ω) ω . In particular we present some independence results which complete the picture of how these perfect set properties relate to each other.

El objetivo de este trabajo es presentar en un solo cuerpo tres maneras de relativizar (o generalizar) el concepto de conjunto constructible de Gödel que no suelen aparecer juntas en la literatura especializada y que son importantes en la Teoría de Conjuntos, por ejemplo para resolver problemas de consistencia o independencia. Presentamos algunos modelos resultantes de las diferentes formas de relativizar el concepto de constructibilidad, sus propiedades básicas y algunas formas débiles del Axioma de Elección válidas o no válidas en (...) ellas. (shrink)

Current climate change has raised concerns over the fate of the stenothermal Antarctic marine fauna (animals that evolved to live in narrow ranges of cold temperatures). The present paper focuses on Notothenioidei, a taxonomic group that dominates Antarctic fish. Notothenioids evolved in the Southern Ocean over the last 20 million years, providing an example of a marine species flock with unique adaptations to the cold at morphological, physiological and biochemical levels. Their phenotypic modifications are often accompanied by ‘irreversible’ genomic losses (...) or gene amplifications. On a micro‐evolutionary scale, relatively ‘shallow’ genetic variation is observed, on account of past fluctuations in population size, and a significant genetic structure is evident, suggesting low population connectivity. These features suggest that Antarctic fish might have relatively little potential to adapt to global warming, at least at a genetic level. The extent of their phenotypic plasticity, which is evident to some degree, awaits further research. (shrink)

Current climate change has raised concerns over the fate of the stenothermal Antarctic marine fauna (animals that evolved to live in narrow ranges of cold temperatures). The present paper focuses on Notothenioidei, a taxonomic group that dominates Antarctic fish. Notothenioids evolved in the Southern Ocean over the last 20 million years, providing an example of a marine species flock with unique adaptations to the cold at morphological, physiological and biochemical levels. Their phenotypic modifications are often accompanied by ‘irreversible’ genomic losses (...) or gene amplifications. On a micro‐evolutionary scale, relatively ‘shallow’ genetic variation is observed, on account of past fluctuations in population size, and a significant genetic structure is evident, suggesting low population connectivity. These features suggest that Antarctic fish might have relatively little potential to adapt to global warming, at least at a genetic level. The extent of their phenotypic plasticity, which is evident to some degree, awaits further research. (shrink)

ABSTRACT In this article we propose to study the way in which the conceptualization of death carried out by Hegel has been read by a series of authors. In this way, in a first section we will restore Heidegger’s interpretation of Hegel to, in a second moment, recover Kojève’s decisive reading of the same author, and end with a replacement of the hermeneutics carried out by Bataille of the German idealist philosopher. Thus, in the conclusion to this article, the existence (...) of repeated and extremely similar motifs present in the three recently named thinkers will be exposed, for whom the figure of Hegel has certainly constituted an unavoidable inheritance. (shrink)

Objective: Fertility loss due to cancer treatment can be a devastating experience for women and the couple. Undergoing fertility preservation can be a complex decision from both a medical and emotional point of view. The aim of the present study was to evaluate which socio-demographic and psychological factors predict a high motivation to undergo fertility preservation.Methods: Fifty-eight female cancer patients who accessed an Oncofertility Unit completed: a questionnaire to collect socio-demographic characteristics and the level of motivation, the Beck-Depression Inventory-II, the (...) State-Trait Anxiety Inventory-Y, and the Fertility Problem Inventory.Results: Almost half of the sample declared a high motivation. At multiple logistic regression analysis only the “Need for parenthood” subscale of the FPI predicted a high motivation. We alternatively evaluated as possible predictor the construct “Representations about the importance of parenthood” in place of the two separate subscales. At multiple logistic regression analysis, only this variable predicted a high motivation to undergo fertility preservation.Conclusion: The most important predictor of a high motivation to undergo fertility preservation is the individual desire for parenthood. This implies that, regardless of socio-demographic characteristics, any woman of childbearing age should receive an appropriate counseling about fertility preservation. (shrink)

Objectives: To foster the development of a privacy-protective, sustainable cross-border information system in the framework of a European public health project. Materials and methods: A targeted privacy impact assessment was implemented to identify the best architecture for a European information system for diabetes directly tapping into clinical registries. Four steps were used to provide input to software designers and developers: a structured literature search, analysis of data flow scenarios or options, creation of an ad hoc questionnaire and conduction of a (...) Delphi procedure. Results: The literature search identified a core set of relevant papers on privacy. Technicians envisaged three candidate system architectures, with associated data flows, to source an information flow questionnaire that was submitted to the Delphi panel for the selection of the best architecture. A detailed scheme envisaging an “aggregation by group of patients” was finally chosen, based upon the exchange of finely tuned summary tables. Conclusions: Public health information systems should be carefully engineered only after a clear strategy for privacy protection has been planned, to avoid breaching current regulations and future concerns and to optimise the development of statistical routines. The BIRO project delivers a specific method of privacy impact assessment that can be conveniently used in similar situations across Europe. (shrink)