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Countable 1-transitive coloured linear orderings II

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Campero-Arena G., Truss J.

Fundamenta Mathematicae

2004

tom 183

nr 3

185-213

This paper gives a structure theorem for the class of countable 1-transitive coloured linear orderings for a countably infinite colour set, concluding the work begun in [1]. There we gave a complete classification of these orders for finite colour sets, of which there are ℵ₁. For infinite colour sets, the details are considerably more complicated, but many features from [1] occur here too, in more marked form, principally the use (now essential it seems) of coding trees, as a means of describing the structures in our list, of which there are now $2^{ℵ₀}$.

Incomparable families and maximal trees

81%

Campero-Arena G., Cancino J., Hrušák M., Miranda-Perea F.

Fundamenta Mathematicae

2016

tom 234

nr 1

73-89

We answer several questions of D. Monk by showing that every maximal family of pairwise incomparable elements of 𝒫(ω)/fin has size continuum, while it is consistent with the negation of the Continuum Hypothesis that there are maximal subtrees of both 𝒫(ω) and 𝒫(ω)/fin of size ω₁.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Campero-Arena G.

1 Cancino J.

1 Hrušák M.

1 Miranda-Perea F.

1 Truss J.

1 2016

1 2004

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Countable 1-transitive coloured linear orderings II

Incomparable families and maximal trees