ISSN:
1572-8730
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Philosophy
Notes:
Abstract A foundational algebra ( $$\mathfrak{B}$$ , f, λ) consists of a hemimorphism f on a Boolean algebra $$\mathfrak{B}$$ with a greatest solution λ to the condition α⩽f(x). The quasi-variety of foundational algebras has a decidable equational theory, and generates the same variety as the complex algebras of structures (X, R), where f is given by R-images and λ is the non-wellfounded part of binary relation R. The corresponding results hold for algebras satisfying λ=0, with respect to complex algebras of wellfounded binary relations. These algebras, however, generate the variety of all ( $$\mathfrak{B}$$ ,f) with f a hemimorphism on $$\mathfrak{B}$$ ). Admitting a second hemimorphism corresponding to the transitive closure of R allows foundational algebras to be equationally defined, in a way that gives a refined analysis of the notion of diagonalisable algebra.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00370431
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