Geodesic
Hypersatisfaction of formulas in agebraic systems
Discussiones Mathematicae. General Algebra and Applications, Tome 29 (2009) no. 2, pp. 123-151.

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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.
Keywords: algebraic system, formula, relational clone, hyperformula 
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Denecke, Klaus; Phusanga, Dara. Hypersatisfaction of formulas in agebraic systems. Discussiones Mathematicae. General Algebra and Applications, Tome 29 (2009) no. 2, pp. 123-151. http://geodesic.mathdoc.fr/item/DMGAA_2009_29_2_a2/

[1] K. Denecke and S.L. Wismath, Hyperidentities and Clones, Gordon and Breach Science Publishers 2000.

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[3] E. Graczyńska and D. Schweigert, Hyperidentities of a given type, Algebra Universalis 27 (1990) 305-318.

[4] J. Koppitz and K. Denecke, M-solid Varieties, Springer 2006.

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[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.