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1

On the automorphism group of the countable dense circular order

100%

Truss J.

Fundamenta Mathematicae

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2009

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tom 204

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nr 2

97-111

EN

Let (C,R) be the countable dense circular ordering, and G its automorphism group. It is shown that certain properties of group elements are first order definable in G, and these results are used to reconstruct C inside G, and to demonstrate that its outer automorphism group has order 2. Similar statements hold for the completion C̅.

2

Countable homogeneous coloured partial orders

68%

de Sousa S., Truss J.

Instytut Matematyczny Polskiej Akademii Nauk

EN

We give a classification of all the countable homogeneous coloured partial orders. This generalizes the similar result in the monochromatic case given by Schmerl.

3

Countable 1-transitive coloured linear orderings II

63%

Campero-Arena G., Truss J.

Fundamenta Mathematicae

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2004

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tom 183

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nr 3

185-213

EN

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 $2^{ℵ₀}$.

Ograniczanie wyników

2 Fundamenta Mathematicae

3 Truss J.

1 Campero-Arena G.

1 de Sousa S.

1 2009

1 2008

1 2004

On the automorphism group of the countable dense circular order

Countable homogeneous coloured partial orders

Countable 1-transitive coloured linear orderings II