Mathematical Sciences: Model Theory and Universal Algebra

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8904014 McKenzie This project is a continuation of work supported by NSF grant No. DMS-8600300. The research lies within the general area of foundations of mathematics, more specifically universal algebra and to some extent, model theory. The research plans of the principal investigator, Ralph McKenzie, include the search for an algebraic characterization of locally finite varieties that possess a decidable theory of finite models, and work on two conjectures concerning, first,the spectrum of cardinalities of subdirectly irreducible algebras in finitely generated varieties, and second, the finite axiomatizability of finitely generated quasivarieties whose algebras possess modular relative congruence lattices.