Decidability of the Natural Numbers with the Almost-All Quantifier

Details Decidability of the Natural Numbers with the Almost-All Quantifier Decidability of the Natural Numbers with the Almost-All Quantifier

2006-02-20

arxiv.org/abs/math/0602415v1

Mathematics

Logic

Scientific paper

We consider the fragment F of first order arithmetic in which quantification
is restricted to ''for all but finitely many.'' We show that the integers form
an F-elementary substructure of the real numbers. Consequently, the F-theory of
arithmetic is decidable.

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