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 T with two halting states μ 0 and μ -1 , an algebra B(T) (finite and of finite type) with the property that the variety generated by B(T) is residually large if T halts in state μ -1 , while if T halts in state μ 0 then this variety is residually bounded by a finite cardinal

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