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- W2019619275 abstract "A uniform, algebraic proof that every number-theoretic assertion provable in any of the intuitionistic theories T listed below has a well-founded recursive proof tree (demonstraby in T ) is given. Thus every such assertion is provable by transfinite induction over some primitive recursive well-ordering. T can be higher order number theory, set theory, or its extensions equiconsistent with large cardinals. It is shown that there is a number-theoretic assertion B ( n ) (independent of T ) with a parameter n such that any primitive recursive linear ordering R on ω for which transfinite induction on R for B ( n ) is provable in T is in fact a well-ordering." @default.
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- W2019619275 date "1985-06-01" @default.
- W2019619275 modified "2023-09-28" @default.
- W2019619275 title "Arithmetic transfinite induction and recursive well-orderings" @default.
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- W2019619275 doi "https://doi.org/10.1016/0001-8708(85)90036-2" @default.
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