Cardinal invariants of the lattice of partitions
We study cardinal coefficients related to combinatorial properties of partitions of with respect to the order of almost containedness.
Barbara Majcher-Iwanow (2000)
Commentationes Mathematicae Universitatis Carolinae
We study cardinal coefficients related to combinatorial properties of partitions of with respect to the order of almost containedness.
Andrzej Rosłanowski, Saharon Shelah (1998)
Fundamenta Mathematicae
We deal with some problems posed by Monk [Mo 1], [Mo 3] and related to cardinal invariants of ultraproducts of Boolean algebras. We also introduce and investigate several new cardinal invariants.
István Juhász, Saharon Shelah, Lajos Soukup, Zoltán Szentmiklóssy (2004)
Fundamenta Mathematicae
We show that if we add any number of Cohen reals to the ground model then, in the generic extension, a locally compact scattered space has at most levels of size ω. We also give a complete ZFC characterization of the cardinal sequences of regular scattered spaces. Although the classes of regular and of 0-dimensional scattered spaces are different, we prove that they have the same cardinal sequences.
Petr A. Biryukov (1980)
Commentationes Mathematicae Universitatis Carolinae
Farah, Ilijas (1998)
Publications de l'Institut Mathématique. Nouvelle Série
Boban Velickovic (1991)
Compositio Mathematica
S. Quickert (2002)
Fundamenta Mathematicae
We show the consistency of CH and the statement “no ccc forcing has the Sacks property” and derive some consequences for ccc -bounding forcing notions.
Paul Larson, Stevo Todorčević (2001)
Fundamenta Mathematicae
We present two varations which create maximal models relative to certain counterexamples to Martin’s Axiom, in hope of separating certain classical statements which fall between MA and Suslin’s Hypothesis. One of these models is taken from [19], in which we maximize relative to the existence of a certain type of Suslin tree, and then force with that tree. In the resulting model, all Aronszajn trees are special and Knaster’s forcing axiom ₃ fails. Of particular interest is the still open question...
Lev Bukovský (1973)
Commentationes Mathematicae Universitatis Carolinae
Menachem Magidor (1978)
Fundamenta Mathematicae
Lev Bukovský (1973)
Fundamenta Mathematicae
Amitayu Banerjee, Zalán Gyenis (2021)
Commentationes Mathematicae Universitatis Carolinae
In set theory without the axiom of choice (AC), we observe new relations of the following statements with weak choice principles. If in a partially ordered set, all chains are finite and all antichains are countable, then the set is countable. If in a partially ordered set, all chains are finite and all antichains have size , then the set has size for any regular . Every partially ordered set without a maximal element has two disjoint cofinal sub sets – CS. Every partially ordered set...
John Truss (1974)
Fundamenta Mathematicae
P. Welch (1988)
Fundamenta Mathematicae
Jörg Brendle, Sakaé Fuchino (2007)
Fundamenta Mathematicae
We study combinatorial principles we call the Homogeneity Principle HP(κ) and the Injectivity Principle IP(κ,λ) for regular κ > ℵ₁ and λ ≤ κ which are formulated in terms of coloring the ordinals < κ by reals. These principles are strengthenings of and of I. Juhász, L. Soukup and Z. Szentmiklóssy. Generalizing their results, we show e.g. that IP(ℵ₂,ℵ₁) (hence also IP(ℵ₂,ℵ₂) as well as HP(ℵ₂)) holds in a generic extension of a model of CH by Cohen forcing, and IP(ℵ₂,ℵ₂) (hence also HP(ℵ₂))...
Jindřich Zapletal (2023)
Commentationes Mathematicae Universitatis Carolinae
It is consistent that ZF + DC holds, the hypergraph of rectangles on a given Euclidean space has countable chromatic number, while the hypergraph of equilateral triangles on does not.
Tomek Bartoszyński (1987)
Fundamenta Mathematicae
B. Balcar, F. Hernández-Hernández, M. Hrušák (2004)
Fundamenta Mathematicae
We study combinatorial properties of the partial order (Dense(ℚ),⊆). To do that we introduce cardinal invariants , , , , , describing properties of Dense(ℚ). These invariants satisfy ≤ ℚ ≤ ℚ ≤ ℚ ≤ ℚ ≤ ℚℚ = pℚ = tℚ = iℚ > hℚ > rnon(M)=min||: ⊆ Dense(R) ∧ (∀I ∈ nwd(R))(∃D ∈ )(I ∩ D = ∅) and cof(M) = min||: ⊆ Dense(ℚ) ∧ (∀I ∈ nwd)(∃D ∈ )(I ∩ = ∅). We use these facts to show that cof(M) ≤ i, which improves a result of S. Shelah.
Kenneth Kunen (2005)
Fundamenta Mathematicae
We consider the cardinal sequences of compact scattered spaces in models where CH is false. We describe a number of models of in which no such space can have ℵ₂ countable levels.
Dow, A., Fremlin, D. (2007)
Acta Mathematica Universitatis Comenianae. New Series