Wyniki wyszukiwania

1

Strong covering without squares

100%

Shelah S.

Fundamenta Mathematicae

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2000

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tom 166

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nr 1-2

87-107

EN

Let W be an inner model of ZFC. Let κ be a cardinal in V. We say that κ-covering holds between V and W iff for all X ∈ V with X ⊆ ON and V ⊨ |X| < κ, there exists Y ∈ W such that X ⊆ Y ⊆ ON and V ⊨ |Y| < κ. Strong κ-covering holds between V and W iff for every structure M ∈ V for some countable first-order language whose underlying set is some ordinal λ, and every X ∈ V with X ⊆ λ and V ⊨ |X| < κ, there is Y ∈ W such that X ⊆ Y ≺ M and V ⊨ |Y| < κ. We prove that if κ is V-regular, $κ^+_V = κ^+_W$, and we have both κ-covering and $κ^+$-covering between W and V, then strong κ-covering holds. Next we show that we can drop the assumption of $κ^+$-covering at the expense of assuming some more absoluteness of cardinals and cofinalities between W and V, and that we can drop the assumption that $κ^+_W = κ^+_V$ and weaken the $κ^+$-covering assumption at the expense of assuming some structural facts about W (the existence of certain square sequences).

2

The pure-projective ideal of a module category

100%

Dowbor P.

Colloquium Mathematicum

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1996

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tom 71

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nr 2

203-215

3

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An approximation algorithm for the total covering problem

100%

Hatami P.

Discussiones Mathematicae Graph Theory

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2007

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tom 27

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nr 3

553-558

EN

We introduce a 2-factor approximation algorithm for the minimum total covering number problem.

4

Realization of primitive branched coverings over closed surfaces following the hurwitz approach

63%

Bogatyi S., Gonçalves D., Kudryavtseva E., Zieschang H.

Open Mathematics

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2003

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tom 1

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nr 2

184-197

EN

Let V be a closed surface, H⊑π1(V) a subgroup of finite index l and D=[A 1,...,A m] a collection of partitions of a given number d≥2 with positive defect v(D). When does there exist a connected branched covering f:W→V of order d with branch data D and f∶W→V It has been shown by geometric arguments [4] that, for l=1 and a surface V different from the sphere and the projective plane, the corresponding branched covering exists (the data D is realizable) if and only if the data D fulfills the Hurwitz congruence v(D)э0 mod 2. In the case l>1, the corresponding branched covering exists if and only if v(D)э0 mod 2, the number d/l is an integer, and each partition A i ∈D splits into the union of l partitions of the number d/l. Here we give a purely algebraic proof of this result following the approach of Hurwitz [11]. The realization problem for the projective plane and l=1 has been solved in [7,8]. The case of the sphere is treated in [1, 2, 12, 7].

Ograniczanie wyników

1 Colloquium Mathematicum

1 Discussiones Mathematicae Graph Theory

1 Fundamenta Mathematicae

1 Open Mathematics

1 Bogatyi S.

1 Dowbor P.

1 Gonçalves D.

1 Hatami P.

1 Kudryavtseva E.

1 Shelah S.

1 Zieschang H.

1 2007

1 2003

1 2000

1 1996

Strong covering without squares

The pure-projective ideal of a module category

An approximation algorithm for the total covering problem

Realization of primitive branched coverings over closed surfaces following the hurwitz approach