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- W4239786980 abstract "By [12] we know that transfinite induction up to Θ εΩ N +1 0 is not provable in ID N , the theory of N -times iterated inductive definitions. In this paper we will show that conversely transfinite induction up to any ordinal less than Θ εΩ N +1 0 is provable in ID N i , the intuitionistic version of ID N , and extend this result to theories for transfinitely iterated inductive definitions. In [14] Schütte proves the wellordering of his notational systems using predicates is wellordered) with M κ ≔ { x ∈ and 0 ≤ κ ≤ N . Obviously the predicates are definable in ID N i with the defining axioms: where Prog [ M κ , X ] means that X is progressive with respect to M κ , i.e. The crucial point in Schütte's wellordering proof is Lemma 19 [14, p. 130] which can be modified to where TI[ M κ + 1 , a ] is the scheme of transfinite induction over M κ + 1 up to a ." @default.
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- W4239786980 date "1978-03-01" @default.
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- W4239786980 title "Provable wellorderings of formal theories for transfinitely iterated inductive definitions" @default.
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- W4239786980 doi "https://doi.org/10.2307/2271954" @default.
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