Geodesic
Existence of a~countable infinite strictly $2$-homogeneous distributive lattice
Matematičeskie trudy, Tome 15 (2012) no. 2, pp. 100-104

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We construct a countable infinite $2$-homogeneous distributive lattice that is not $3$-homogeneous, which answers a question of Droste and Macpherson. 
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     author = {K. Zh. Kudaǐbergenov},
     title = {Existence of a~countable infinite strictly $2$-homogeneous distributive lattice},
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K. Zh. Kudaǐbergenov. Existence of a~countable infinite strictly $2$-homogeneous distributive lattice. Matematičeskie trudy, Tome 15 (2012) no. 2, pp. 100-104. http://geodesic.mathdoc.fr/item/MT_2012_15_2_a5/