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On the limit existence principles in elementary arithmetic and Σn0-consequences of theories
2005
Annals of Pure and Applied Logic
We study the arithmetical schema asserting that every eventually decreasing elementary recursive function has a limit. Some other related principles are also formulated. We establish their relationship with restricted parameter-free induction schemata. We also prove that the same principle, formulated as an inference rule, provides an axiomatization of the Σ 2 -consequences of IΣ 1 . Using these results we show that ILM is the logic of Π 1 -conservativity of any reasonable extension of
doi:10.1016/j.apal.2005.05.005
fatcat:gkxbfaxtircybhyh5p4n2hooku