Categorical Abstract Algebraic Logic: Local Characterization Theorems for Classes of Systems
Titel:
Categorical Abstract Algebraic Logic: Local Characterization Theorems for Classes of Systems
Auteur:
Voutsadakis, George
Verschenen in:
Communications in algebra
Paginering:
Jaargang 36 (2008) nr. 8 pagina's 3093-3112
Jaar:
2008-08
Inhoud:
Let L = 〈F, R, ρ〉 be a system language. Given a class of L-systems K and an L-algebraic system A = 〈SEN,〈N,F〉〉, i.e., a functor SEN: Sign → Set, with N a category of natural transformations on SEN, and F:F → N a surjective functor preserving all projections, define the collection KA of A-systems in K as the collection of all members of K of the form = 〈 SEN,〈N,F〉,R〉, for some set of relation systems R on SEN. Taking after work of Czelakowski and Elgueta in the context of the model theory of equality-free first-order logic, several relationships between closure properties of the class K, on the one hand, and local properties of KA and global properties connecting KA and KA', whenever there exists an L-morphism 〈 F,α〉 : A → A', on the other, are investigated. In the main result of the article, it is shown, roughly speaking, that KA is an algebraic closure system, for every L-algebraic system A, provided that K is closed under subsystems and reduced products.
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