VARIETIES WITH COFINAL SETS - EXAMPLES AND AMALGAMATION

A variety V has a confinal set S subset-of V if any A is-an-element-of V is embeddable in a reduced product of members of S. Amalgamation in and examples of such varieties are considered. Among other results, the following are proved: (i) every lattice is embeddable in an ultraproduct of finite partition lattices; (ii) if V is a residually small, congruence distributive variety whose members all have one-element subalgebras, then the amalgamation class of V is closed under finite products.