On Free {\omega}-Continuous and Regular Ordered Algebras
نویسندگان
چکیده
Let E be a set of inequalities between finite Σ-terms. Let Vω and Vr denote the varieties of all ω-continuous ordered Σ-algebras and regular ordered Σ-algebras satisfying E, respectively. We prove that the free Vr-algebra R(X) on generators X is the subalgebra of the corresponding free Vω-algebra Fω(X) determined by those elements of Fω(X) denoted by the regular Σ-coterms. We actually establish this fact as a special case of a more general construction for families of algebras specified by syntactically restricted completeness and continuity properties. Thus our result is also applicable to ordered regular algebras of higher order.
منابع مشابه
On Free ω-Continuous and Regular Ordered Algebras
Let E be a set of inequalities between finite Σ-terms. Let Vω and Vr denote the varieties of all ω-continuous ordered Σ-algebras and regular ordered Σ-algebras satisfying E, respectively. We prove that the free Vr-algebra R(X) on generators X is the subalgebra of the corresponding free Vω-algebra Fω(X) determined by those elements of Fω(X) denoted by the regular Σ-coterms. We actually establish...
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