Tue, 06 Feb 2024, 1:25 pm MT
Let A be a finite simple non-abelian Mal'cev algebra (e.g. a group, loop, ring). We identify the Fraisse limit D of the class of finite direct powers of A as a filtered Boolean power of A by the countable atomless Boolean algebra B and show that D also arises as congruence classes of the countable free algebra in the variety generated by A.
Further we show that filtered Boolean powers of A by B are omega-categorical, have the small index property, strong uncountable cofinality and the Bergman property.
This is joint work with Nik Ruskuc.