The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “Borel and Baire reducibility”

Partition properties of ω1 compatible with CH

Uri Abraham, Stevo Todorčević (1997)

Fundamenta Mathematicae

Similarity:

A combinatorial statement concerning ideals of countable subsets of ω is introduced and proved to be consistent with the Continuum Hypothesis. This statement implies the Suslin Hypothesis, that all (ω, ω*)-gaps are Hausdorff, and that every coherent sequence on ω either almost includes or is orthogonal to some uncountable subset of ω.

A dichotomy theorem for mono-unary algebras

Su Gao (2000)

Fundamenta Mathematicae

Similarity:

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

Borel extensions of Baire measures

J. Aldaz (1997)

Fundamenta Mathematicae

Similarity:

We show that in a countably metacompact space, if a Baire measure admits a Borel extension, then it admits a regular Borel extension. We also prove that under the special axiom ♣ there is a Dowker space which is quasi-Mařík but not Mařík, answering a question of H. Ohta and K. Tamano, and under P(c), that there is a Mařík Dowker space, answering a question of W. Adamski. We answer further questions of H. Ohta and K. Tamano by showing that the union of a Mařík space and a compact space...

Expansions of the real line by open sets: o-minimality and open cores

Chris Miller, Patrick Speissegger (1999)

Fundamenta Mathematicae

Similarity:

The open core of a structure ℜ := (ℝ,<,...) is defined to be the reduct (in the sense of definability) of ℜ generated by all of its definable open sets. If the open core of ℜ is o-minimal, then the topological closure of any definable set has finitely many connected components. We show that if every definable subset of ℝ is finite or uncountable, or if ℜ defines addition and multiplication and every definable open subset of ℝ has finitely many connected components, then the open core...

Almost all submaximal groups are paracompact and σ-discrete

O. Alas, I. Protasov, M. Tkačenko, V. Tkachuk, R. Wilson, I. Yaschenko (1998)

Fundamenta Mathematicae

Similarity:

We prove that any topological group of a non-measurable cardinality is hereditarily paracompact and strongly σ-discrete as soon as it is submaximal. Consequently, such a group is zero-dimensional. Examples of uncountable maximal separable spaces are constructed in ZFC.

Two dichotomy theorems on colourability of non-analytic graphs

Vladimir Kanovei (1997)

Fundamenta Mathematicae

Similarity:

We prove:  Theorem 1. Let κ be an uncountable cardinal. Every κ-Suslin graph G on reals satisfies one of the following two requirements: (I) G admits a κ-Borel colouring by ordinals below κ; (II) there exists a continuous homomorphism (in some cases an embedding) of a certain locally countable Borel graph G 0 into G.  Theorem 2. In the Solovay model, every OD graph G on reals satisfies one of the following two requirements: (I) G admits an OD colouring by countable ordinals; (II) as above. ...

The σ-ideal of closed smooth sets does not have the covering property

Carlos Uzcátegui (1996)

Fundamenta Mathematicae

Similarity:

We prove that the σ-ideal I(E) (of closed smooth sets with respect to a non-smooth Borel equivalence relation E) does not have the covering property. In fact, the same holds for any σ-ideal containing the closed transversals with respect to an equivalence relation generated by a countable group of homeomorphisms. As a consequence we show that I(E) does not have a Borel basis.