dmitri83's Mariano:HL [1 article]

Abstract

We establish the following model-theoretic characterization: profinite $L$-structures, the cofiltered limits of finite $L$-structures,are retracts of ultraproducts of finite $L$-structures. As a consequence, any elementary class of $L$-structures axiomatized by $L$-sentences of the form $∀ ecx (ψ_0(ecx) \ra ψ_1(ecx))$, where $ψ_0(ecx),ψ_1(ecx)$ are existencial-positives $L$-formulas, is closed under the formation of profinite objects in the category L-mod, the category of structures suitable for the language $L$ and $L$-homomorphisms. ...