Add to ORKGWe determine exact consistency strengths for various failures of the Singular Cardinals Hypothesis (SCH) in the setting of the Zermelo-Fraenkel axiom system ZF without the Axiom of Choice (AC). By the new notion of parallel Prikry forcing that we introduce, we obtain surjective failures of SCH using only one measurable cardinal, including a surjective failure of Shelah’s pcf theorem about the size of the power set of ℵω. Using symmetric collapses t
In this paper we analyze the PCF structure of a generic extension by the main forcing from our previ...
We prove a number of consistency results complementary to the ZFC results from our paper [4]. We pro...
International audienceThe axioms ZFC of first order set theory are one of the best and most widely a...
Abstract. We describe a framework for proving consistency results about singular cardinals of arbitr...
Abstract. The purpose of this paper is to present some results which suggest that the Singular Cardi...
Abstract. We describe a framework for proving consistency re-sults about singular cardinals of arbit...
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 20...
AbstractWe show that o(k) = k++ is necessary for ¬SCH. Together with previous results it provides th...
We prove that Galvin's property consistently fails at successors of strong limit singular cardinals....
Set theory has made tremendous progress in the last 75 years, but much of it has been outside the bo...
We say that κ is µ-hypermeasurable (or µ-strong) for a cardinal µ ≥ κ+ if there is an embedding j: V...
AbstractWe show that o(k) = k++ is necessary for ¬SCH. Together with previous results it provides th...
In this paper we analyze the PCF structure of a generic extension by the main forcing from our previ...
Abstract. We construct a model in which the singular cardinal hypothesis fails at ℵω. We use charact...
We show that the consistency of the theory “ZF + DC + Every successor cardinal is regular + Every li...
In this paper we analyze the PCF structure of a generic extension by the main forcing from our previ...
We prove a number of consistency results complementary to the ZFC results from our paper [4]. We pro...
International audienceThe axioms ZFC of first order set theory are one of the best and most widely a...
Abstract. We describe a framework for proving consistency results about singular cardinals of arbitr...
Abstract. The purpose of this paper is to present some results which suggest that the Singular Cardi...
Abstract. We describe a framework for proving consistency re-sults about singular cardinals of arbit...
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 20...
AbstractWe show that o(k) = k++ is necessary for ¬SCH. Together with previous results it provides th...
We prove that Galvin's property consistently fails at successors of strong limit singular cardinals....
Set theory has made tremendous progress in the last 75 years, but much of it has been outside the bo...
We say that κ is µ-hypermeasurable (or µ-strong) for a cardinal µ ≥ κ+ if there is an embedding j: V...
AbstractWe show that o(k) = k++ is necessary for ¬SCH. Together with previous results it provides th...
In this paper we analyze the PCF structure of a generic extension by the main forcing from our previ...
Abstract. We construct a model in which the singular cardinal hypothesis fails at ℵω. We use charact...
We show that the consistency of the theory “ZF + DC + Every successor cardinal is regular + Every li...
In this paper we analyze the PCF structure of a generic extension by the main forcing from our previ...
We prove a number of consistency results complementary to the ZFC results from our paper [4]. We pro...
International audienceThe axioms ZFC of first order set theory are one of the best and most widely a...