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The initial meadows. (English) Zbl 1217.68142

Meadows, introduced about a decade ago by Bergstra and Tucker, provide a total algebra alternative for fields. In short, a meadow is a commutative ring with an inverse for multiplication which has 0 as a fixed point. This paper develops the initial meadow of characteristic 0 and proves a normal-form theorem for it. Immediate consequences are the decidability of the closed-term problem for meadows and the computability of their initial object.

MSC:

68Q65 Abstract data types; algebraic specification
03B25 Decidability of theories and sets of sentences
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