All posts by Sławek

Orbit-finite dimensional vector spaces, and orbit-finite systems of linear equations

Here is some naive questions that came to one’s mind when considering vector spaces where the dimension is not finite but orbit-finite: under a reasonable assumption on atoms \mathbb A, say \omega-categoricity,

— is it true that every vector subspace of an orbit-finite dimensional vector space is orbit-finite dimensional?

— is it true that the set of solutions of an orbit-finite  system of linear equations is orbit-finite dimensional?

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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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