Geodesic
The Tarski-Lindenbaum algebra of the class of all prime strongly constructivizable models of algorithmic dimension one
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 913-922

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We study the class of all prime strongly constructivizable models of algorithmic dimension $1$ in a fixed finite rich signature. It is proved that the Tarski-Lindenbaum algebra of this class considered together with a Gödel numbering of the sentences is a Boolean $\Pi^0_3$-algebra whose computable ultrafilters form a dense subset in the set of all ultrafilters; moreover, this algebra is universal with respect to the class of Boolean $\Sigma^0_2$-algebras whose computable ultrafilters represent a dense subset in the set of arbitrary ultrafilters in the algebra. This gives a characterization to the Tarski-Lindenbaum algebra of the class of all prime strongly constructivizable models of algorithmic dimension $1$ in a fixed finite rich signature.
Keywords: first-order logic, Tarski-Lindenbaum algebra, computable isomorphism, semantic class of models, algorithmic complexity estimate. 
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     author = {M. G. Peretyat'kin},
     title = {The {Tarski-Lindenbaum} algebra of the class of all prime strongly constructivizable models of algorithmic dimension one},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {913--922},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
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     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a17/}
}
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M. G. Peretyat'kin. The Tarski-Lindenbaum algebra of the class of all prime strongly constructivizable models of algorithmic dimension one. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 913-922. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a17/