On the Gitik–Shelah theorem
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Ryszard Frankiewicz
Abstract
The well-known Gitik–Shelah theorem (1989) touches the problem of existence isomorphisms between some quotient algebras. In this paper, we study a relation between the existence of such isomorphisms and the existence of so-called Kuratowski partitions of adequate Baire spaces. For this purpose, we give strictly combinatorial methods.
Dedicated to Prof. Alexander Kharazishvili
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Articles in the same Issue
- Frontmatter
- On absolutely Baire nonmeasurable functions
- Existence of special rainbow triangles in weak geometries
- Images of Bernstein sets via continuous functions
- Square-integrable representations and multipliers
- Semigroups of pathological sets
- Points of density and ideals of subsets of ℕ
- On Kharazishvili type measures in infinite-dimensional Polish vector spaces
- Families of symmetric Cantor sets from the category and measure viewpoints
- On the Gitik–Shelah theorem
- On equidistant lines of given line configurations
- On convergence of sequences of functions possessing closed graphs
- On combinatorial and set-theoretical aspects of some finite and infinite point sets
- On Kuratowski partitions in the Marczewski and Laver structures and Ellentuck topology
- Automorphism groups of mono-unary algebras and CH
- On topologies related to the extension of the Lebesgue measure
- An abstract formulation of a theorem of Sierpiński on the nonmeasurable sum of two measure zero sets
- Local affine selections of convex set-valued functions
- On orbits without the Baire property
- Mann iteration process for monotone nonexpansive mappings with a graph
- Mixing coded systems
- Methods of comparison of families of real functions in porosity terms
Articles in the same Issue
- Frontmatter
- On absolutely Baire nonmeasurable functions
- Existence of special rainbow triangles in weak geometries
- Images of Bernstein sets via continuous functions
- Square-integrable representations and multipliers
- Semigroups of pathological sets
- Points of density and ideals of subsets of ℕ
- On Kharazishvili type measures in infinite-dimensional Polish vector spaces
- Families of symmetric Cantor sets from the category and measure viewpoints
- On the Gitik–Shelah theorem
- On equidistant lines of given line configurations
- On convergence of sequences of functions possessing closed graphs
- On combinatorial and set-theoretical aspects of some finite and infinite point sets
- On Kuratowski partitions in the Marczewski and Laver structures and Ellentuck topology
- Automorphism groups of mono-unary algebras and CH
- On topologies related to the extension of the Lebesgue measure
- An abstract formulation of a theorem of Sierpiński on the nonmeasurable sum of two measure zero sets
- Local affine selections of convex set-valued functions
- On orbits without the Baire property
- Mann iteration process for monotone nonexpansive mappings with a graph
- Mixing coded systems
- Methods of comparison of families of real functions in porosity terms
