Electronic Resource
Springer
Algebra universalis
18 (1984), S. 308-326
ISSN:
1420-8911
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract An infinite algebra is locally complete if its local closure is the set of all finitary operations. We give a local completeness criterion in terms of a system R of finitary relations on A such that the polymorph Pol ρ of each ρ εR is locally incomplete and for every locally incomplete algebra 〈A; F〉 we have F ⊑ Pol ρ for some ρ ε R. This system consists of (i) certain natural relations whose polymorphs are best possible in the sense that they are co-atoms in the lattice of locally closed incomplete algebras, (ii) five types of binary relations, (iii) one type of ternary relations and (iv) at least ternary totally reflexive and symmetric relations that are not locally central.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01203368
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