# Atomic compactness for reflexive graphs

Fundamenta Mathematicae (1999)

- Volume: 162, Issue: 2, page 99-117
- ISSN: 0016-2736

## Access Full Article

top## Abstract

top## How to cite

topDelhommé, Christian. "Atomic compactness for reflexive graphs." Fundamenta Mathematicae 162.2 (1999): 99-117. <http://eudml.org/doc/212419>.

@article{Delhommé1999,

abstract = {A first order structure $$ with universe M is atomic compact if every system of atomic formulas with parameters in M is satisfiable in $$ provided each of its finite subsystems is. We consider atomic compactness for the class of reflexive (symmetric) graphs. In particular, we investigate the extent to which “sparse” graphs (i.e. graphs with “few” vertices of “high” degree) are compact with respect to systems of atomic formulas with “few” unknowns, on the one hand, and are pure restrictions of their Stone-Čech compactifications, on the other hand.},

author = {Delhommé, Christian},

journal = {Fundamenta Mathematicae},

keywords = {sparse graphs; reflexive graphs; first-order structure; atomic compactness; systems of atomic formulas; Stone-Čech compactifications},

language = {eng},

number = {2},

pages = {99-117},

title = {Atomic compactness for reflexive graphs},

url = {http://eudml.org/doc/212419},

volume = {162},

year = {1999},

}

TY - JOUR

AU - Delhommé, Christian

TI - Atomic compactness for reflexive graphs

JO - Fundamenta Mathematicae

PY - 1999

VL - 162

IS - 2

SP - 99

EP - 117

AB - A first order structure $$ with universe M is atomic compact if every system of atomic formulas with parameters in M is satisfiable in $$ provided each of its finite subsystems is. We consider atomic compactness for the class of reflexive (symmetric) graphs. In particular, we investigate the extent to which “sparse” graphs (i.e. graphs with “few” vertices of “high” degree) are compact with respect to systems of atomic formulas with “few” unknowns, on the one hand, and are pure restrictions of their Stone-Čech compactifications, on the other hand.

LA - eng

KW - sparse graphs; reflexive graphs; first-order structure; atomic compactness; systems of atomic formulas; Stone-Čech compactifications

UR - http://eudml.org/doc/212419

ER -

## References

top- [1] E. Corominas, Sur les ensembles ordonnés projectifs et la propriété du point fixe, C. R. Acad. Sci. Paris Sér. I 311 (1990), 199-204. Zbl0731.06001
- [2] C. Delhommé, Propriétés de projection, thèse, Université Claude Bernard-Lyon I, 1995.
- [3] C. Delhommé, Infinite projection properties, Math. Logic Quart. 44 (1998), 481-492. Zbl0922.03049
- [4] S. Hazan, On triangle-free projective graphs, Algebra Universalis 35 (1996), 185-196. Zbl0845.05062
- [5] R. McKenzie and S. Shelah, The cardinals of simple models for universal theories, in: Proc. Sympos. Pure Math. 25, Amer. Math. Soc., 1971, 53-74.
- [6] J. Mycielski, Some compactifications of general algebras, Colloq. Math. 13 (1964), 1-9. Zbl0136.26102
- [7] J. Mycielski and C. Ryll-Nardzewski, Equationally compact algebras II, Fund. Math. 61 (1968), 271-281.
- [8] W. Taylor, Atomic compactness and graph theory, ibid. 65 (1969), 139-145. Zbl0182.34401
- [9] W. Taylor, Compactness and chromatic number, ibid. 67 (1970), 147-153. Zbl0199.30401
- [10] W. Taylor, Some constructions of compact algebras, Ann. Math. Logic 3 (1971), 395-435. Zbl0239.08003
- [11] W. Taylor, Residually small varieties, Algebra Universalis 2 (1972), 33-53. Zbl0263.08005
- [12] B. Węglorz, Equationally compact algebras (I), Fund. Math. 59 (1966), 289-298. Zbl0221.02039
- [13] F. Wehrung, Equational compactness of bi-frames and projection algebras, Algebra Universalis 33 (1995), 478-515. Zbl0830.08005
- [14] G. Wenzel, Equational compactness, Appendix 6 in: G. Grätzer, Universal Algebra, 2nd ed., Springer, 1979.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.