Displaying similar documents to “Chains and antichains in Boolean algebras”

Embedding partially ordered sets into ω ω

Ilijas Farah (1996)

Fundamenta Mathematicae

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We investigate some natural questions about the class of posets which can be embedded into ⟨ω,≤*⟩. Our main tool is a simple ccc forcing notion H E which generically embeds a given poset E into ⟨ω,≤*⟩ and does this in a “minimal” way (see Theorems 9.1, 10.1, 6.1 and 9.2).

A dichotomy theorem for mono-unary algebras

Su Gao (2000)

Fundamenta Mathematicae

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We study the isomorphism relation of invariant Borel classes of countable mono-unary algebras and prove a strong dichotomy theorem.

Luzin and anti-Luzin almost disjoint families

Judith Roitman, Lajos Soukup (1998)

Fundamenta Mathematicae

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Under M A ω 1 every uncountable almost disjoint family is either anti-Luzin or has an uncountable Luzin subfamily. This fails under CH. Related properties are also investigated.

Gaussian automorphisms whose ergodic self-joinings are Gaussian

Mariusz Lemańczyk, F. Parreau, J. Thouvenot (2000)

Fundamenta Mathematicae

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 We study ergodic properties of the class of Gaussian automorphisms whose ergodic self-joinings remain Gaussian. For such automorphisms we describe the structure of their factors and of their centralizer. We show that Gaussian automorphisms with simple spectrum belong to this class.  We prove a new sufficient condition for non-disjointness of automorphisms giving rise to a better understanding of Furstenberg's problem relating disjointness to the lack of common factors....