Tag Archives: arbitrary atoms

Join of two elements

Let be two elements with atoms. The pair  satisfies the following universal property: supports both and , and if is another element with this property, then supports .

We demonstrate the existence of an element denoted , with a dual property: is supported both by and by , and if is another element with this property, then is supported by .  The construction does not require any assumptions on the symmetry.

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Color-preserving automorphisms in Fraisse classes (new version)

Again, a question closely related to a characterization of standard atoms (not to be confused with standard alphabets:). The question is a refinement of a question posted in Automorphisms vs color-preserving automorphisms in Fraisse classes, which has been answered negatively (see the recent post The colored open question closed).

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