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The notes which follow reflect the content of a two day tutorial which took place at the Fields Institute on 5/29 and 5/30 in 2009. Most of the content has existed in the literature for some time (pri...
FORCING AXIOMS AND THE CONTINUUM HYPOTHESIS,PART II:TRANSCENDING ω1-SEQUENCES OF REAL NUMBERS
FORCING AXIOMS CONTINUUM HYPOTHESIS TRANSCENDING ω1-SEQUENCES OF REAL NUMBERS
2015/8/17
The purpose of this article is to prove that the forcing axiom for completely proper forcings is inconsistent with the Continuum Hypothesis. This answers a longstanding problem of Shelah.
One way to formulate the Baire Category Theorem is that no compact space can be covered by countably many nowhere dense sets. Soon after Cohen’s discovery of forcing, it was realized that it was natur...
Under the Continuum Hypothesis all nonreflexive Banach space ultrapowers are primary
Banach space ultrapowers primary Banach spaces Stone-Cech remainder Representation Theorem superreflexivity
2011/8/30
Abstract: In this note a large class of primary Banach spaces is characterized. Namely, it will be demonstrated that under the Continuum Hypothesis the ultrapower of any infinite dimensional nonsuperr...
Some Representation Theorem for nonreflexive Banach space ultrapowers under the Continuum Hypothesis
Banach space ultrapowers Stone-Cech remainder dual space extreme points smooth points complemented subspaces
2011/8/31
Abstract: In this paper it will be shown that assuming the Continuum Hypothesis (CH) every nonreflexive Banach space ultrapower is isometrically isomorphic to the space of continuous, bounded and real...
Deciding the Continuum Hypothesis with the Inverse Power Set
Continuum Hypothesis the Inverse Power Set
2010/11/9
We introduce the concept of inverse power set by adding two axioms to the Zermelo-Fraenkel set theory. This extends the Zermelo-Fraenkel set theory with a new type of set. We present different ways to...