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On families of Lindelöf and related subspaces of 2 ω

Lúcia Junqueira, Piotr Koszmider (2001)

Fundamenta Mathematicae

We consider the families of all subspaces of size ω₁ of 2 ω (or of a compact zero-dimensional space X of weight ω₁ in general) which are normal, have the Lindelöf property or are closed under limits of convergent ω₁-sequences. Various relations among these families modulo the club filter in [ X ] ω are shown to be consistently possible. One of the main tools is dealing with a subspace of the form X ∩ M for an elementary submodel M of size ω₁. Various results with this flavor are obtained. Another tool used...

On isomorphism classes of C ( 2 [ 0 , α ] ) spaces

Elói Medina Galego (2009)

Fundamenta Mathematicae

We provide a complete isomorphic classification of the Banach spaces of continuous functions on the compact spaces 2 [ 0 , α ] , the topological sums of Cantor cubes 2 , with smaller than the first sequential cardinal, and intervals of ordinal numbers [0,α]. In particular, we prove that it is relatively consistent with ZFC that the only isomorphism classes of C ( 2 [ 0 , α ] ) spaces with ≥ ℵ₀ and α ≥ ω₁ are the trivial ones. This result leads to some elementary questions on large cardinals.

On iterated forcing for successors of regular cardinals

Todd Eisworth (2003)

Fundamenta Mathematicae

We investigate the problem of when ≤λ-support iterations of < λ-complete notions of forcing preserve λ⁺. We isolate a property- properness over diamonds-that implies λ⁺ is preserved and show that this property is preserved by λ-support iterations. Our condition is a relative of that presented by Rosłanowski and Shelah in [2]; it is not clear if the two conditions are equivalent. We close with an application of our technology by presenting a consistency result on uniformizing colorings of ladder...

On level by level equivalence and inequivalence between strong compactness and supercompactness

Arthur W. Apter (2002)

Fundamenta Mathematicae

We prove two theorems, one concerning level by level inequivalence between strong compactness and supercompactness, and one concerning level by level equivalence between strong compactness and supercompactness. We first show that in a universe containing a supercompact cardinal but of restricted size, it is possible to control precisely the difference between the degree of strong compactness and supercompactness that any measurable cardinal exhibits. We then show that in an unrestricted size universe...

On reflection of stationary sets

Q. Feng, Menachem Magidor (1992)

Fundamenta Mathematicae

We show that there are stationary subsets of uncountable spaces which do not reflect.

On the existence of group localizations under large-cardinal axioms.

Carles Casacuberta, Dirk Scevenels (2001)

RACSAM

Uno de los problemas abiertos más antiguos de la teoría de grupos categórica es si todo par ortogonal (formado por una clase de grupos y una clase de homomorfismos que se determinan mutuamente por ortogonalidad en el sentido de Freyd-Kelly), se halla asociado a un funtor de localización. Se sabe que esto es cierto si se acepta la validez de un cierto axioma de cardinales grandes (el principio de Vopenka), pero no se conoce ninguna demostración mediante los axiomas ordinarios (ZFC) de la teoría de...

On the nontrivial solvability of systems of homogeneous linear equations over in ZFC

Jan Šaroch (2020)

Commentationes Mathematicae Universitatis Carolinae

Motivated by the paper by H. Herrlich, E. Tachtsis (2017) we investigate in ZFC the following compactness question: for which uncountable cardinals κ , an arbitrary nonempty system S of homogeneous -linear equations is nontrivially solvable in provided that each of its subsystems of cardinality less than κ is nontrivially solvable in ?

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