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2-ary atoms assume atom of Fn+k(T automorphism axiom of choice binary relation Boolean algebra choice can fail Cohen Cornell University corollary to Proposition countable model countable set CrC a countable define an order Definition dense linear order disjoint union distinct elements Dl Dn finite partial order finite sequence finitely consistent formula of ZF formula with parameters formulas of L(T Hence infinite model infinite subset infinite well ordered isomorphism j e uu Let ox linearly ordered model of TQ n-ary relation n+k)-homogeneous non-algebraic categorical theory order diagram ordered pairs ordered set ordered subset parameters linear order prime model Proof Q.E.D. Corollary ramified language relational system Ryll-Nardzewski S_'s satisfy sequence of distinct Set Theory Suppose T-compatible T-type T-type(a Theorem total order extending ultrafilter uu-homogeneous Vaught vector space want to thank XQ-categorical yr,xr ZF with parameters