Displaying similar documents to “Nonmetrizable topological dynamical characterization of central sets”

Rotation sets for subshifts of finite type

Krystyna Ziemian (1995)

Fundamenta Mathematicae

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For a dynamical system (X,f) and a function φ : X → ℝ N the rotation set is defined. The case when (X,f) is a transitive subshift of finite type and φ depends on the cylinders of length 2 is studied. Then the rotation set is a convex polyhedron. The rotation vectors of periodic points are dense in the rotation set. Every interior point of the rotation set is a rotation vector of an ergodic measure.

Interpreting reflexive theories in finitely many axioms

V. Shavrukov (1997)

Fundamenta Mathematicae

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For finitely axiomatized sequential theories F and reflexive theories R, we give a characterization of the relation ’F interprets R’ in terms of provability of restricted consistency statements on cuts. This characterization is used in a proof that the set of ∏ 1 (as well as ∑ 1 ) sentences π such that GB interprets ZF+π is Σ 3 0 -complete.

Linear orders and MA + ¬wKH

Zoran Spasojević (1995)

Fundamenta Mathematicae

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I prove that the statement that “every linear order of size 2 ω can be embedded in ( ω ω , ≪ ) ” is consistent with MA + ¬ wKH.

Loop spaces and homotopy operations

David Blanc (1997)

Fundamenta Mathematicae

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We describe an obstruction theory for an H-space X to be a loop space, in terms of higher homotopy operations taking values in π * X . These depend on first algebraically “delooping” the Π-algebras π * X , using the H-space structure on X, and then trying to realize the delooped Π-algebra.

Bohr compactifications of discrete structures

Joan Hart, Kenneth Kunen (1999)

Fundamenta Mathematicae

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We prove the following theorem: Given a⊆ω and 1 ≤ α < ω 1 C K , if for some η < ℵ 1 and all u ∈ WO of length η, a is Σ α 0 ( u ) , then a is Σ α 0 .We use this result to give a new, forcing-free, proof of Leo Harrington’s theorem: Σ 1 1 -Turing-determinacy implies the existence of 0 .

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).

On entropy of patterns given by interval maps

Jozef Bobok (1999)

Fundamenta Mathematicae

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Defining the complexity of a green pattern exhibited by an interval map, we give the best bounds of the topological entropy of a pattern with a given complexity. Moreover, we show that the topological entropy attains its strict minimum on the set of patterns with fixed eccentricity m/n at a unimodal X-minimal case. Using a different method, the last result was independently proved in[11].