# Hypersatisfaction of formulas in agebraic systems

Discussiones Mathematicae - General Algebra and Applications (2009)

- Volume: 29, Issue: 2, page 123-151
- ISSN: 1509-9415

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topKlaus Denecke, and Dara Phusanga. "Hypersatisfaction of formulas in agebraic systems." Discussiones Mathematicae - General Algebra and Applications 29.2 (2009): 123-151. <http://eudml.org/doc/276867>.

@article{KlausDenecke2009,

abstract = {In [2] the theory of hyperidentities and solid varieties was extended to algebraic systems and solid model classes of algebraic systems. The disadvantage of this approach is that it needs the concept of a formula system. In this paper we present a different approach which is based on the concept of a relational clone. The main result is a characterization of solid model classes of algebraic systems. The results will be applied to study the properties of the monoid of all hypersubstitutions of an ordered algebra.},

author = {Klaus Denecke, Dara Phusanga},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {algebraic system; formula; relational clone; hyperformula; hypersubstitution; hypersatisfaction},

language = {eng},

number = {2},

pages = {123-151},

title = {Hypersatisfaction of formulas in agebraic systems},

url = {http://eudml.org/doc/276867},

volume = {29},

year = {2009},

}

TY - JOUR

AU - Klaus Denecke

AU - Dara Phusanga

TI - Hypersatisfaction of formulas in agebraic systems

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2009

VL - 29

IS - 2

SP - 123

EP - 151

AB - In [2] the theory of hyperidentities and solid varieties was extended to algebraic systems and solid model classes of algebraic systems. The disadvantage of this approach is that it needs the concept of a formula system. In this paper we present a different approach which is based on the concept of a relational clone. The main result is a characterization of solid model classes of algebraic systems. The results will be applied to study the properties of the monoid of all hypersubstitutions of an ordered algebra.

LA - eng

KW - algebraic system; formula; relational clone; hyperformula; hypersubstitution; hypersatisfaction

UR - http://eudml.org/doc/276867

ER -

## References

top- [1] K. Denecke and S.L. Wismath, Hyperidentities and Clones, Gordon and Breach Science Publishers 2000. Zbl0960.08001
- [2] K. Denecke and D. Phusanga, Hyperformulas and Solid Algebraic Systems, Studia Logica 90 (2) (2008) 263-286. Zbl1162.08001
- [3] E. Graczyńska and D. Schweigert, Hyperidentities of a given type, Algebra Universalis 27 (1990) 305-318. Zbl0715.08002
- [4] J. Koppitz and K. Denecke, M-solid Varieties, Springer 2006.
- [5] A.I. Mal'cev, Algebraic Systems, Akademie-Verlag, Berlin 1973.
- [6] R. Pöschel and L.A. Kalužnin, Funktionen-und Relationenalgebren, VEB Deutscher Verlag der Wissenschaften, Berlin 1979.
- [7] J.A. Goguen and R.M. Burstall, Introducing Institution, in Proceeding of the Logic of Programming Workshop (1984) 221-256.
- [8] J.A. Goguen and R.M. Burstall, Institutions: Abstract Model Theory for Specification and Programming, Journal of the ACM 39 (1) (1992) 95-146. Zbl0799.68134

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