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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 non-extendibility of strongness and supercompactness through strong compactness

Arthur W. Apter (2002)

Fundamenta Mathematicae

If κ is either supercompact or strong and δ < κ is α strong or α supercompact for every α < κ, then it is known δ must be (fully) strong or supercompact. We show this is not necessarily the case if κ is strongly compact.

On the nontrivial solvability of systems of homogeneous linear equations over $ℤ$ 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 $ℤ$ -linear equations is nontrivially solvable in $ℤ$ provided that each of its subsystems of cardinality less than $κ$ is nontrivially solvable in $ℤ$ ?

On the Rank of Ext.

Martin Huber, Paul C. Eklof (1980)

Mathematische Zeitschrift

On weak Normality and Selectivity of Ultrafilters

A. Joanovic΄, Z. Mijajlovic΄ (1993)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

On weakly rigid monounary algebras

Danica Jakubíková-Studenovská (1980)

Mathematica Slovaca

On σ-complete prime ideals in Boolean algebras

Karel Prikry (1971)

Colloquium Mathematicae

On $ω^{2}$ -saturated families

Lajos Soukup (1991)

Commentationes Mathematicae Universitatis Carolinae

If there is no inner model with measurable cardinals, then for each cardinal $λ$ there is an almost disjoint family $𝒜_{λ}$ of countable subsets of $λ$ such that every subset of $λ$ with order type $\geq ω^{2}$ contains an element of $𝒜_{λ}$ .

Openly generated Boolean algebras and the Fodor-type reflection principle

Sakaé Fuchino, Assaf Rinot (2011)

Fundamenta Mathematicae

We prove that the Fodor-type Reflection Principle (FRP) is equivalent to the assertion that any Boolean algebra is openly generated if and only if it is ℵ₂-projective. Previously it was known that this characterization of openly generated Boolean algebras follows from Axiom R. Since FRP is preserved by c.c.c. generic extension, we conclude in particular that this characterization is consistent with any set-theoretic assertion forcable by a c.c.c. poset starting from a model of FRP. A crucial step...

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