Abstract
In this chapter we will find necessary and sufficient conditions for a locally finite, strongly Abelian variety V to be decidable. It will turn out that for such varieties, the properties of being undecidable, hereditarily undecidable, unstructured, or ω-unstructured, all coincide. The results of Chapter 11 reduce the problem to determining those locally finite, essentially unary, k-sorted varieties (for k ≥ 1) which are decidable. For the purposes of determining the decidability of V, we may assume that V is in fact a multi-unary k-sorted variety of finite type. Thus each term in the language of V has at most one variable.
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© 1989 Birkhäuser Boston, Inc.
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McKenzie, R., Valeriote, M. (1989). The unary case. In: Structure of Decidable Locally Finite Varieties. Progress in Mathematics, vol 79. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4552-0_13
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DOI: https://doi.org/10.1007/978-1-4612-4552-0_13
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8908-1
Online ISBN: 978-1-4612-4552-0
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