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- W2468740159 abstract "For $mathbf{A}leqmathbf{B}$ first order structures in a class $mathcal{K}$, say that $mathbf{A}$ is an epic substructure of $mathbf{B}$ in $mathcal{K}$ if for every $mathbf{C}inmathcal{K}$ and all homomorphisms $g,g^{prime}:mathbf{B}rightarrowmathbf{C}$, if $g$ and $g'$ agree on $A$, then $g=g'$. We prove that $mathbf{A}$ is an epic substructure of $mathbf{B}$ in a class $mathcal{K}$ closed under ultraproducts if and only if $A$ generates $mathbf{B}$ via operations definable in $mathcal{K}$ with primitive positive formulas. Applying this result we show that a quasivariety of algebras $mathcal{Q}$ with an $n$-ary near-unanimity term has surjective epimorphisms if and only if $mathbb{SP}_{n}mathbb{P}_{u}(mathcal{Q}_{RSI})$ has surjective epimorphisms. It follows that if $mathcal{F}$ is a finite set of finite algebras with a common near-unanimity term, then it is decidable whether the (quasi)variety generated by $mathcal{F}$ has surjective epimorphisms." @default.
- W2468740159 created "2016-07-22" @default.
- W2468740159 creator A5004342195 @default.
- W2468740159 date "2016-07-11" @default.
- W2468740159 modified "2023-09-27" @default.
- W2468740159 title "Epic substructures and primitive positive functions" @default.
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- W2468740159 hasPublicationYear "2016" @default.
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