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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{MZM_2021_110_6_a3,
     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/}
}
TY  - JOUR
AU  - I. A. Gorbunov
TI  - Theories of the Classical Propositional Logic and Substitutions
JO  - Matematičeskie zametki
PY  - 2021
SP  - 856
EP  - 864
VL  - 110
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2021_110_6_a3/
LA  - ru
ID  - MZM_2021_110_6_a3
ER  - 
%0 Journal Article
%A I. A. Gorbunov
%T Theories of the Classical Propositional Logic and Substitutions
%J Matematičeskie zametki
%D 2021
%P 856-864
%V 110
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2021_110_6_a3/
%G ru
%F MZM_2021_110_6_a3
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/

[1] R. Wojcicki, Lectures on Propositional Calculi, Ossolineum Publ., Wroclaw, 1984 | MR

[2] R. Wojcicki, Lectures on Propositional Calculi, , 1984 http://sl.fr.pl/wojcicki/Wojcicki-Lectures.pdf

[3] M. Esteban, Duality theory and Abstract Algebraic Logic, Thesis, Universitat de Barcelona, Barcelona, 2013

[4] M. Tokarz, “Connections between some notions of completeness of structural propositional calculi”, Studia Logica, 32 (1973), 77–89 | DOI | MR