The axiom of choice for linearly ordered families
On the automorphism group of the countable dense circular order
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.
Countable 1-transitive coloured linear orderings II
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...
Countable homogeneous coloured partial orders
We give a classification of all the countable homogeneous coloured partial orders. This generalizes the similar result in the monochromatic case given by Schmerl.
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