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Dec 25, 2014 at 8:02 comment added მამუკა ჯიბლაძე Thank you for the accurate answer! I will try to add to mine more details about what does this approach give in the infinite case.
Dec 24, 2014 at 23:51 comment added porton The condition 3 is motivated by the fact that "principal staroids" (staroids corresponding to $n$-ary relations in a certain way) are always upper sets. But I am interested in both cases: with and without axiom 3.
Dec 24, 2014 at 23:48 history answered Todd Trimble CC BY-SA 3.0