Decidability of the Natural Numbers with the Almost-All Quantifier
classification
🧮 math.LO
math-phmath.MP
keywords
arithmeticnumbersalmost-allconsequentlyconsiderdecidabilitydecidablef-elementary
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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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