Geodesic
Theories of the Classical Propositional Logic and Substitutions
Matematičeskie zametki, Tome 110 (2021) no. 6, pp. 856-864

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For any propositional logic, Sushko's lemma states that, for any substitution, the preimage of the set of all tautologies of this logic is its theory. The problem of the relationship between the set of all such preimages and the set of all theories for classical propositional logic is considered. It is proved that any consistent theory of classical logic is the preimage of the set of all identically true formulas for some substitution. An algorithm for constructing such a substitution for any consistent finitely axiomatizable theory is presented.
Keywords: theories of classical propositional logic
Mots-clés : inversion of substitutions. 
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     author = {I. A. Gorbunov},
     title = {Theories of the {Classical} {Propositional} {Logic} and {Substitutions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {856--864},
     publisher = {mathdoc},
     volume = {110},
     number = {6},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_110_6_a3/}
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I. A. Gorbunov. Theories of the Classical Propositional Logic and Substitutions. Matematičeskie zametki, Tome 110 (2021) no. 6, pp. 856-864. http://geodesic.mathdoc.fr/item/MZM_2021_110_6_a3/