Timeline for Can transfinite induction be defined as axiom scheme in FOL on bin-tree structures?
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| Aug 12, 2010 at 23:03 | comment | added | Lucas K. | Schoppenhauer, Very much thanks for the answer, but unfortunately this was not what I was looking for. I made an edit to the question. I hope it is more clear now. Once you have defined ordinals, you can add the axiom scheme as you suggested. This gives a FOL that is stronger than standard FOL + PA, because with ordinals you can prove Goodstein's theorem, while FOL + PA can not (according to reversed mathematics). But I don't want to add ordinals. Instead I want to add binary trees and an axiom scheme, in such way that it is as strong as the system with ordinals. | |
| Aug 12, 2010 at 3:38 | history | answered | Christoph-Simon Senjak | CC BY-SA 2.5 |