Relation algebra reducts of cylindric algebras and complete representations
Robin Hirsch · Journal of Symbolic Logic · 2007
Abstract We show, for any ordinalγ≥ 3, that the classℜaCAγis pseudo-elementary and has a recursively enumerable elementary theory. ScKdenotes the class of strong subalgebras of members of the classK. We devise games,Fn(3 ≤n≤ω),G, H, and show, for an atomic relation algebra with countably many atoms, that for 3 ≤n 5 and any classKof relation algebras satisfying thatKis not closed under subalgebras and is not elementary. For infiniteγ, the inclusion ℜaCAγ⊂ScℜaCAγis strict. For infiniteγand for a countable relation algebra we show that has a complete representation if and only if is atomic and ∃ has a winning strategy inF(At( )) if and only if is atomic and ∈ScℜaCAγ.