Separating club-guessing principles in the presence of fat forcing axioms

We separate various weak forms of Club Guessing at $\omega_1$ in the presence of $2^{\aleph_0}$ large, Martin's Axiom, and related forcing axioms. We also answer a question of Abraham and Cummings concerning the consistency of the failure of a certain polychromatic Ramsey statement together with the continuum large. All these models are generic extensions via finite support iterations with symmetric systems of structures as side conditions, possibly enhanced with $\omega$-sequences of predicates, and in which the iterands are taken from a relatively small class of forcing notions. We also prove that the natural forcing for adding a large symmetric system of structures (the first member in all our iterations) adds $\aleph_1$-many reals but preserves CH

Forcing consequences of PFA together with the continuum large

We develop a new method for building forcing iterations with symmetric systems of structures as side conditions. Using our method we prove that the forcing axiom for the class of all the small finitely proper posets is compatible with a large continuum.Comment: 35 page

Measuring club-sequences together with the continuum large

Measuring says that for every sequence (C_\delta)_{\delta\aleph_2. The construction works over any model of ZFC + CH and can be described as a finite support forcing iteration with systems of countable models as side conditions and with symmetry constraints imposed on its initial segments. One interesting feature of this iteration is that it adds dominating functions $f:\omega_1\longrightarrow\omega_1$ mod. countable at each of its stages

Long reals

The familiar continuum R of real numbers is obtained by a well-known procedure which, starting with the set of natural numbers N=\omega, produces in a canonical fashion the field of rationals Q and, then, the field R as the completion of Q under Cauchy sequences (or, equivalently, using Dedekind cuts). In this article, we replace \omega by any infinite suitably closed ordinal \kappa in the above construction and, using the natural (Hessenberg) ordinal operations, we obtain the corresponding field \kappa-R, which we call the field of the \kappa-reals. Subsequently, we study the properties of the various fields \kappa-R and develop their general theory, mainly from the set-theoretic perspective. For example, we investigate their connection with standard themes such as forcing and descriptive set theory

El Foc com a causant de canvis en les propietat del sòl : incendis forestals i cremes prescrites

L'article ens aproxima als resultats d'un estudi de recerca que es fixa en l'evolució de l'espai públic del barri del Mercadal de Girona, i més concretament en les tres places que s'hi ubiquen: Constitució, Josep Pla i Santa Susanna. Després de vint anys de l'inici de la transformació urbanística del barri, es fa una anàlisi de com aquestes tres places són percebudes i viscudes per les persones que hi habiten, especialment des d'una perspectiva de gènere.El artículo nos aproxima a los resultados de una investigación que se fija en la evolución del espacio público del barrio del Mercadal de Gerona, y más concretamente en las tres plazas que existen: Constitució, Josep Pla y Santa Susanna. Después de veinte años del inicio de la transformación urbanística del barrio, se realiza un análisis sobre como se perciben estas tres plazas y como las viven las personas que las habitan, especialmente desde una perspectiva de género.This paper presents the results of a research project focused in the evolution of the public space of the Mercadal neighborhood of Girona, and more precisely in the three squares that are located there: Constitució, Josep Pla and Santa Susana. After twenty years of urban regeneration in the neighborhood, these three spaces are analyzed from the point of view of the people that live there and experience them, specially from a gender perspective