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Basic S and L : The existence of an S-space under MA and $\neg$ CH
Basic S and L : The existence of an S-space under MA and $\neg$ CHandrejko
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This document discusses S and L spaces, which are topological spaces that have certain separation and density properties. It summarizes key results about the existence of S and L spaces under different set theory assumptions, such as the existence of S and L spaces under the continuum hypothesis but their destruction under Martin's Axiom and the negation of the continuum hypothesis. The document also outlines proofs of the consistency of the existence of an S space under Martin's Axiom and the negation of the continuum hypothesis.
diccionario de la web2.0 para ongOlga Berrios
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Este documento presenta una lista de t辿rminos clave relacionados con el Web 2.0, incluyendo agregadores, blogactivismo, copyleft, brecha digital, folksonom鱈a, Google, larga cola, periodismo 3.0, intercambio, memes, redes sociales, valoraci坦n social, Wikipedia, formatos XML y YouTube.Killing S Spaces
Killing S Spacesandrejko
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The document discusses separable spaces and killing separability. It defines a separable space as one containing a countable dense subset and a right separated space as one containing an uncountable subspace where subsets up to any countable ordinal are open. The author is Erik Andrejko from the University of Wisconsin-Madison and the document is dated March 25, 2008.The relative consistency of the negation of the Axiom of Choice using permuta...
The relative consistency of the negation of the Axiom of Choice using permuta...andrejko
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This document discusses the axiom of choice (AC) and related principles in set theory. It makes the following key points:
1. AC allows proving the existence of sets without explicit construction, which some early mathematicians found controversial.
2. AC is equivalent to several other principles like Zorn's lemma and is needed to prove certain paradoxical theorems.
3. Various weaker forms of choice exist, like the axiom of dependent choice, and some principles like the prime ideal theorem do not imply full AC.
4. Models of set theory without AC, called permutation models, can be constructed, showing the consistency of denying AC is independent of Zermelo-Fraenkel set theory
Edificis Romansmarg
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Los edificios romanos m叩s importantes incluyen arcos de triunfo, acueductos, templos, foros, teatros, circos, anfiteatros, coliseos y termas. Tambi辿n construyeron murallas defensivas alrededor de ciudades como Tarragona y Le坦n.More Related Content
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Edificis Romansmarg
油
Los edificios romanos m叩s importantes incluyen arcos de triunfo, acueductos, templos, foros, teatros, circos, anfiteatros, coliseos y termas. Tambi辿n construyeron murallas defensivas alrededor de ciudades como Tarragona y Le坦n.