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)

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.

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)

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)

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)

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.

Facts happen at every interaction, but they are not absolute: they are relative to the systems involved in the interaction. Stable facts are those whose relativity can effectively be ignored. In this work, we describe how stable facts emerge in a world of relative facts and discuss their respective roles in connecting quantum theory and the world. The distinction between relative and stable facts resolves the difficulties pointed out by the no-go theorem of Frauchiger and Renner, and is consistent with (...) the experimental violation of the Local Friendliness inequalities of Bong et al.. Basing the ontology of the theory on relative facts clarifies the role of decoherence in bringing about the classical world and solves the apparent incompatibility between the ‘linear evolution’ and ‘projection’ postulates. (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)

Based on existing moral philosophy, Carlo Prisco introduces Eusebism as a way to develop new perspectives on being and relating by offering practical tools to approach everyday life and transfer good thought into action.

This book argues that vegetarian and vegan people should be guaranteed the right to eat according to their beliefs. The author claims that the right to vegetarianism is backed by the human and civil rights recognized in the constitutions of several nations.