Displaying similar documents to “List of Paul Erdős's publications in number theory”

Reverse mathematics of some topics from algorithmic graph theory

Peter Clote, Jeffry Hirst (1998)

Fundamenta Mathematicae

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This paper analyzes the proof-theoretic strength of an infinite version of several theorems from algorithmic graph theory. In particular, theorems on reachability matrices, shortest path matrices, topological sorting, and minimal spanning trees are considered.

Each nowhere dense nonvoid closed set in Rn is a σ-limit set

Andrei Sivak (1996)

Fundamenta Mathematicae

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We discuss main properties of the dynamics on minimal attraction centers (σ-limit sets) of single trajectories for continuous maps of a compact metric space into itself. We prove that each nowhere dense nonvoid closed set in n , n ≥ 1, is a σ-limit set for some continuous map.

The Dugundji extension property can fail in ωµ -metrizable spaces

Ian Stares, Jerry Vaughan (1996)

Fundamenta Mathematicae

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We show that there exist ω μ -metrizable spaces which do not have the Dugundji extension property ( 2 ω 1 with the countable box topology is such a space). This answers a question posed by the second author in 1972, and shows that certain results of van Douwen and Borges are false.

On backward stability of holomorphic dynamical systems

Genadi. Levin (1998)

Fundamenta Mathematicae

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For a polynomial with one critical point (maybe multiple), which does not have attracting or neutral periodic orbits, we prove that the backward dynamics is stable provided the Julia set is locally connected. The latter is proved to be equivalent to the non-existence of a wandering continuum in the Julia set or to the shrinking of Yoccoz puzzle-pieces to points.

A classification of definable forcings on ω1

Jindřich Zapletal (1997)

Fundamenta Mathematicae

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Under the assumption of the existence of sharps for reals all simply definable posets on ω 1 are classified up to forcing equivalence.