Geodesic
Some properties of solutions of equations in a~free semigroup
Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part V, Tome 32 (1972), pp. 21-28

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Among other results i t is proved that some recursive set $M$ cannot be represented in the form $$ a\in M\Leftrightarrow\exists x_1\cdots x_n(P=Q), $$ where $P=Q$ is an equation in the free semigroup. 
@article{ZNSL_1972_32_a3,
     author = {N. K. Kossovski},
     title = {Some properties of solutions of equations in a~free semigroup},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {21--28},
     publisher = {mathdoc},
     volume = {32},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1972_32_a3/}
}
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N. K. Kossovski. Some properties of solutions of equations in a~free semigroup. Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part V, Tome 32 (1972), pp. 21-28. http://geodesic.mathdoc.fr/item/ZNSL_1972_32_a3/