The initial meadows. (English) Zbl 1217.68142

Bethke, Inge; Rodenburg, Piet

J. Symb. Log. 75, No. 3, 888-895 (2010).

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.

Reviewer: Răzvan Diaconescu (Ploiesti)

MSC:

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

Keywords:

data structures; specification languages; initial algebra semantics; word problem; decidability; computable algebras; normal forms

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