Atomic compactness for reflexive graphs

Christian Delhommé

Fundamenta Mathematicae (1999)

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

Abstract

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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.

How to cite

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Delhommé, 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

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  10. [10] W. Taylor, Some constructions of compact algebras, Ann. Math. Logic 3 (1971), 395-435. Zbl0239.08003
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  12. [12] B. Węglorz, Equationally compact algebras (I), Fund. Math. 59 (1966), 289-298. Zbl0221.02039
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