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

Few new reals

We introduce a new method for building models of CH, together with $\Pi_2$ statements over $H(\omega_2)$, by forcing over a model of CH. Unlike similar constructions in the literature, our construction adds new reals, but only $\aleph_1$-many of them. Using this approach, we prove that a very strong form of the negation of Club Guessing at $\omega_1$ known as Measuring is consistent together with CH, thereby answering a well-known question of Moore. The construction works over any model of ZFC + CH and can be described as a finite support forcing construction with finite systems of countable models with markers as side conditions and with strong symmetry constraints on both side conditions and working parts

RELACIONES ECOLOGICAS EN LA TRAMA DE LA PELÍCULA SENDEROS DE LA MENTE

El ambiente, se compone de elementos vivos y no vivos, y aunque cada uno de ellos se presenta en la naturaleza de forma individual, estos, en general, se encuentran conectados en un mundo de relaciones, en una red de interconexiones ecológicas y, de cualquier forma, son estas conexiones de manera sistémica, las que orientan el desarrollo humano endógeno sustentable. Esta primicia eco-sistémica, condujo a realizar esta reseña, cuyo propósito es contribuir con criticidad a la sensibilización y concienciación del lector, a través de la aprehensión y comprensión de las interconexiones ecológicas y sus implicaciones para el desarrollo en sistemas humanizados. Para ello, se plantea develar las interconexiones o relaciones ecológicas que subyacen en la trama de la película Mindwalk -Senderos de la Mente- que se estrenó desde el 9 de septiembre de 1990, basada en el pensamiento ecologista del físico cuántico Fritjof Capra tomado de su libro El Punto de Inflexión: La ciencia, la sociedad y la cultura en ascenso publicado en 1982. Se presenta como un estudio hermenéutico interpretativo, cuyo análisis se realiza a partir de observaciones sobre su escenografía presentada y los contenidos evocados por cada una de sus personajes, sin descartar los elementos representativos de la misma naturaleza. Se logra una abstracción de conexiones como; la relación ser humano - mundo de la vida, las conexiones entre política, física y metafísica, la relación geohistórica del espacio geográfico, el ambiente como ente vivo sustentador de la vida y una reflexión profunda que exige cambios hacia una nueva sociedad

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

On the Consistency Strength of MM(ω1\omega_1)

We prove that the consistency strength of Martin's Maximum restricted to partial orders of cardinality $\omega_1$ follows from the consistency of ZFC

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

A Generalization of Martin's Axiom

We define the $\aleph_{1.5}$ chain condition. The corresponding forcing axiom is a generalization of Martin's Axiom and implies certain uniform failures of club--guessing on $\omega_1$ that don't seem to have been considered in the literature before.Comment: 36 page