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Countable homogeneous lattices Truss, John


(joint work with Aisha Abogatma) Previously a rather short list of countable homogeneous lattices was known, including, apart from the one-point lattice and the rationals, the countable universal-homogeneous distributive lattice and one or two others arising from amalgamations of certain classes of lattices. We show that there are in fact uncountably many countable homogeneous lattices. Our examples are all non-modular, and the natural question to ask is whether every countable homogeneous modular lattice is necessarily distributive, a conjecture which has recently been proved by Christian Herrmann. Our method also applies to show that certain other classes of structures also have uncountably many countable homogeneous members.

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