Remarks on Herbrand normal forms and Herbrand realizations |
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| Authors: | Ulrich Kohlenbach |
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| Affiliation: | 1. Fachbereich Mathematik, J.W. Goethe-Universit?t, Robert-Mayer-Strasse 6-10, W-6000, Frankfurt am Main, Federal Republic of Germany
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| Abstract: | LetAH be the Herbrand normal form ofA andAH,D a Herbrand realization ofAH. We show| (i) | There is an example of an (open) theory  + with function parameters such that for someA not containing function parameters | | (ii) | Similar for first order theories + if the index functions used in definingAH are permitted to occur in instances of non-logical axiom schemata of , i.e. for suitable ,A | | (iii) | In fact, in (1) we can take for + the fragment ( 10-IA)+ of second order arithmetic with induction restricted to10-formulas, and in (2) we can take for the fragment (10,b-IA) of first order arithmetic with induction restricted to formulas VxA(x) whereA contains only bounded quantifiers. | | (iv) | On the other hand,
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