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A theories of classical propositional logic and counterimages of substitutions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2020), pp. 26-29 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study theories based on the classical propositional logic. It follows from the lemma of Sushko's that for any classical propositional theory $T$ and substitution function $\varepsilon$ of formulas instead of propositional variables, the set $\varepsilon^{-1}(T)$ is also a classical propositional theory. In the paper, it is proved the following statement being more strong: for any consistent finitely axiomatized classical propositional theory $T$ there exists a substitution function $\varepsilon$ such that $T$ is a preimage of the set of all tautologies under $\varepsilon$. An algorithm of constructing of such a substitution function is given.
Keywords: lattice of theories of classical propositional logic, counterimages of substitutions, Suszko's lemma.
Mots-clés : unification 
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     title = {A theories of classical propositional logic and counterimages of substitutions},
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I. A. Gorbunov. A theories of classical propositional logic and counterimages of substitutions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2020), pp. 26-29. http://geodesic.mathdoc.fr/item/IVM_2020_1_a2/

[1] Wójcicki R., Lectures on propositional calculi www.studialogica.org/wojcicki

[2] Wójcicki R., Lectures on propositional calculi, Ossolineum, Wroclaw, 1984 | MR | Zbl