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1

A partition theorem for α-large sets

100%

Bigorajska T., Kotlarski H.

Fundamenta Mathematicae

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1999

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tom 160

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nr 1

27-37

EN

Working with Hardy hierarchy and the notion of largeness determined by it, we define the notion of a partition of a finite set of natural numbers $A=∪_{i

2

Some combinatorics involving ξ-large sets

100%

Bigorajska T., Kotlarski H.

Fundamenta Mathematicae

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2002

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tom 175

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nr 2

119-125

EN

We prove a version of the Ramsey theorem for partitions of (increasing) n-tuples. We derive this result from a version of König's infinity lemma for ξ-large trees. Here ξ < ε₀ and the notion of largeness is in the sense of Hardy hierarchy.

3

On regular interstices and selective types in countable arithmetically saturated models of Peano Arithmetic

81%

Bigorajska T., Kotlarski H., Schmerl J. H.

Fundamenta Mathematicae

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1998

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tom 158

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nr 2

125-146

EN

We continue the earlier research of [1]. In particular, we work out a class of regular interstices and show that selective types are realized in regular interstices. We also show that, contrary to the situation above definable elements, the stabilizer of an element inside M(0) whose type is selective need not be maximal.

4

Functions provably total in $I^{-}Σ_{n}$

60%

Adamowicz Z., Bigorajska T.

Fundamenta Mathematicae

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1989

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tom 132

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nr 3

189-194

Ograniczanie wyników

4 Fundamenta Mathematicae

4 Bigorajska T.

3 Kotlarski H.

1 Adamowicz Z.

1 Schmerl J. H.

1 2002

1 1999

1 1998

1 1989

A partition theorem for α-large sets

Some combinatorics involving ξ-large sets

On regular interstices and selective types in countable arithmetically saturated models of Peano Arithmetic

Functions provably total in $I^{-}Σ_{n}$