Restricted Interpolation and the Projective Beth Property in Equational Logic
Algebra i logika, Tome 42 (2003) no. 6, pp. 712-726.

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

Interconnections between syntactic and categorical properties of equational theories are established. The notions of restricted interpolation and of restricted amalgamation are introduced and their equivalence proved; interrelations of the above-mentioned properties and the projective Beth property, interpolation, and amalgamation are studied.
Keywords: equational logic, restricted interpolation, restricted amalgamation, projective Beth property.
@article{AL_2003_42_6_a4,
     author = {L. L. Maksimova},
     title = {Restricted {Interpolation} and the {Projective} {Beth} {Property} in {Equational} {Logic}},
     journal = {Algebra i logika},
     pages = {712--726},
     publisher = {mathdoc},
     volume = {42},
     number = {6},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2003_42_6_a4/}
}
TY  - JOUR
AU  - L. L. Maksimova
TI  - Restricted Interpolation and the Projective Beth Property in Equational Logic
JO  - Algebra i logika
PY  - 2003
SP  - 712
EP  - 726
VL  - 42
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2003_42_6_a4/
LA  - ru
ID  - AL_2003_42_6_a4
ER  - 
%0 Journal Article
%A L. L. Maksimova
%T Restricted Interpolation and the Projective Beth Property in Equational Logic
%J Algebra i logika
%D 2003
%P 712-726
%V 42
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2003_42_6_a4/
%G ru
%F AL_2003_42_6_a4
L. L. Maksimova. Restricted Interpolation and the Projective Beth Property in Equational Logic. Algebra i logika, Tome 42 (2003) no. 6, pp. 712-726. http://geodesic.mathdoc.fr/item/AL_2003_42_6_a4/

[1] L. L. Maksimova, “Intuitionistic logic and implicit definability”, Ann. Pure Appl. Logic, 105 (2000), 1–3 | DOI | MR | Zbl

[2] D. Pigozzi, “Amalgamation, congruence extension and interpolation properties in algebras”, Algebra Univers., 1:3 (1972), 269–349 | MR | Zbl

[3] I. Sain, “Beth's and Craig's properties via epimorphisms and amalgamation in algebraic logic”, Algebraic logic and universal algebra in computer science, Lect. Notes Comput. Sci., 425, eds. C. H. Bergman, R. D. Maddux, D. I. Pigozzi, Springer-Verlag, Berlin, 1990, 209–226 | MR

[4] L. L. Maksimova, “Modalnye logiki i mnogoobraziya modalnykh algebr: svoistvo Beta, interpolyatsiya i amalgamiruemost”, Algebra i logika, 31:2 (1992), 145–166 | MR | Zbl

[5] J. Czelakowski, D. Pigozzi, “Amalgamation and interpolation in abstract algebraic logic”, Models, algebras and proofs., Sel. papers X Latin Am. Symp. math. logic held Bogota, Lect. Notes Pure Appl. Math., 203, eds. X. Caicedo, C. H. Montenegro, Marcel Dekker, New York, 1999, 187–265 | MR | Zbl

[6] A. Wronski, “On a form of equational interpolation property”, Foundations of logic and linguistics, Problems and solution, sel. contrib. 7th Intern. Congr., Plenum Press, London, 1985, 23–29 | MR

[7] L. Maksimova, “Explicit and implicit definability in modal and related logics”, Bull. Sect. Log., Univ. Bodź, Dep. Log., 27:1/2 (1998), 36–39

[8] E. Hoogland, Definability and interpolation. Model-theoretic investigations, ILLC Dissertation Series DS-2001-05, Amsterdam, 2001

[9] Model-Theoretic Logics, eds. J. Barwise, S. Feferman, Springer-Verlag, New York, 1985 | MR

[10] P. D. Bacsich, “Amalgamation properties and interpolation theorems for equational theories”, Algebra Univers., 5:1 (1975), 45–55 | DOI | MR | Zbl

[11] B. Jonsson, “Extensions of relational structures”, Theory of models, Proc. 1963 Intern. Symp. Berkeley, North-Holland, Amsterdam, 1965, 146–157 | MR

[12] H. Ono, “Interpolation and the Robinson property for logics not closed under the Boolean operations”, Algebra Univers., 23:2 (1986), 111–122 | DOI | MR | Zbl

[13] L. L. Maksimova, “Proektivnye svoistva Beta v modalnykh i superintuitsionistskikh logikakh”, Algebra i logika, 38:3 (1999), 316–333 | MR | Zbl

[14] A. I. Maltsev, Algebraicheskie sistemy, Nauka, M., 1970 | MR

[15] G. Grätzer, H. Lakser, “The structure of pseudocomplemented distributive lattices. II: Congruence extension and amalgamation”, Trans. Am. Math. Soc., 156 (1971), 343–358 | DOI | MR | Zbl

[16] T. Kowalski, H. Ono, “Splittings in the variety of residuated lattices”, Algebra Univers., 44 (2000), 283–298 | DOI | MR | Zbl