Timeline for Can a universal induction rule be formulated?
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| Nov 28, 2016 at 23:29 | comment | added | Lucas K. | Thanks for the answer. However, it was not my intention to beat ZFC. Indeed ZFC can do it all, but the idea of Hilbert's program is to give a justification of the more complex logics. Although ZFC is good in formalizing mathematics, and I do not doubt the consistency, but from a foundation point of view it lacks any elegance, in my opinion. That the natural numbers are well-ordered can be expressed and proven in a meta-level on top of PA. But this meta-level doesn't allow it to use in induction. So, my idea is to find a formal way to incorporate meta-level into the logic to get the succession. | |
| Nov 27, 2016 at 23:53 | history | answered | Noah Schweber | CC BY-SA 3.0 |