Geodesic
Axiomatizability and completeness of some classes of partially ordered polygons
Algebra i logika, Tome 48 (2009) no. 1, pp. 90-121.

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

We study partially ordered monoids over which a class of free (over sets and over posets), projective, and (strongly, weakly) flat partially ordered polygons is axiomatizable, complete, or model complete. Similar issues for polygons were dealt with in papers by V. Gould and A. Stepanova.
Keywords: partially ordered monoid, class of partially ordered polygons, axiomatizable class, model complete class, complete class. 
@article{AL_2009_48_1_a3,
     author = {M. A. Pervukhin and A. A. Stepanova},
     title = {Axiomatizability and completeness of some classes of partially ordered polygons},
     journal = {Algebra i logika},
     pages = {90--121},
     publisher = {mathdoc},
     volume = {48},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2009_48_1_a3/}
}
TY  - JOUR
AU  - M. A. Pervukhin
AU  - A. A. Stepanova
TI  - Axiomatizability and completeness of some classes of partially ordered polygons
JO  - Algebra i logika
PY  - 2009
SP  - 90
EP  - 121
VL  - 48
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2009_48_1_a3/
LA  - ru
ID  - AL_2009_48_1_a3
ER  - 
%0 Journal Article
%A M. A. Pervukhin
%A A. A. Stepanova
%T Axiomatizability and completeness of some classes of partially ordered polygons
%J Algebra i logika
%D 2009
%P 90-121
%V 48
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2009_48_1_a3/
%G ru
%F AL_2009_48_1_a3
M. A. Pervukhin; A. A. Stepanova. Axiomatizability and completeness of some classes of partially ordered polygons. Algebra i logika, Tome 48 (2009) no. 1, pp. 90-121. http://geodesic.mathdoc.fr/item/AL_2009_48_1_a3/

[1] A. A. Stepanova, “Aksiomatiziruemost i polnota nekotorykh klassov $S$-poligonov”, Algebra i logika, 30:5 (1991), 583–594 | MR | Zbl

[2] V. Gould, “Axiomatisability problems for $S$-systems”, J. Lond. Math. Soc. II Ser., 35 (1987), 193–201 | DOI | MR | Zbl

[3] S. Bulman-Fleming, V. Gould, “Axiomatisability of weakly flat, flat and projective $S$-acts”, Commun. Algebra, 30:11 (2002), 5575–5593 | DOI | MR | Zbl

[4] X. Shi, “Strongly flat and po-flat $S$-posets”, Commun. Algebra, 33:12 (2005), 4515–4531 | DOI | MR | Zbl

[5] J. B. Fountain, “Perfect semigroups”, Proc. Edinb. Math. Soc. II Ser., 20 (1976), 87–93 | DOI | MR | Zbl

[6] G. Keisler, Ch. Chen, Teoriya modelei, Mir, M., 1977 | MR

[7] P. Gabriel, M. Tsisman, Kategorii chastnykh i teoriya gomologii, Mir, M., 1971 | Zbl

[8] X. Shi, Z. Liu, F. Wang, S. Bulman-Fleming, “Indecomposable, projective and flat $S$-posets”, Commun. Algebra, 33:1 (2005), 235–251 | DOI | MR | Zbl

[9] M. Kilp, U. Knauer, A. V. Mikhalev, “Monoids, acts and categories. With applications to wreath products and graphs. A handbook for students and researchers”, de Gruyter Expo. Math., 29, Walter de Gruyter, Berlin, 2000 | MR | Zbl

[10] J. R. Isbell, “Perfect monoids”, Semigroup Forum, 2 (1971), 95–118 | DOI | MR | Zbl

[11] S. Bulman-Fleming, V. Laan, “Lazard's theorem for $S$-posets”, Math. Nachr., 278:15 (2005), 1743–1755 | DOI | MR | Zbl