@article {IOPORT.06078048, author = {Ganchev, Hristo and Soskova, Mariya}, title = {Embedding distributive lattices in the $\Sigma ^{0}_{2}$ enumeration degrees.}, year = {2012}, journal = {Journal of Logic and Computation}, volume = {22}, number = {4}, issn = {0955-792X}, pages = {779-792}, publisher = {Oxford University Press, Oxford}, doi = {10.1093/logcom/exq042}, abstract = {Summary: We prove that every countable distributive lattice is embeddable in the $\Sigma ^{0}_{2}$ enumeration degrees via a 0-1 preserving monomorphism. Moreover, we prove that every countable distributive lattice is embeddable below arbitrary $\Delta ^{0}_{2}$ degree via a 0 preserving monomorphism.}, identifier = {06078048}, }