Geodesic
The set of closed classes $P_{k+1}$ that can be homomorphically mapped on $P_k$ has the cardinality of continuum
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2020), pp. 69-70

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We prove that the partially ordered set $\mathcal{L}^{k+1}_{k}$ of all closed classes of $(k+1)$-valued logic which can be homomorphically mapped onto $k$-valued logic has the cardinality of continuum. 
@article{VMUMM_2020_1_a10,
     author = {L. Yu. Devyatkin},
     title = {The set of closed classes $P_{k+1}$ that can be homomorphically mapped on $P_k$ has the cardinality of continuum},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {69--70},
     publisher = {mathdoc},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2020_1_a10/}
}
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L. Yu. Devyatkin. The set of closed classes $P_{k+1}$ that can be homomorphically mapped on $P_k$ has the cardinality of continuum. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2020), pp. 69-70. http://geodesic.mathdoc.fr/item/VMUMM_2020_1_a10/