Recursive Inseparability for Residual Bounds of Finite Algebras

Journal of Symbolic Logic 65 (4):1863-1880 (2000)
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Abstract

We exhibit a construction which produces for every Turing machine $\mathcal{T}$ with two halting states $\mu_0$ and $\mu_{-1}$, an algebra B with the property that the variety generated by B is residually large if $\mathcal{T}$ halts in state $\mu_{-1}$, while if $\mathcal{T}$ halts in state $\mu_0$ then this variety is residually bounded by a finite cardinal.

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