My past research interests included differential algebraic equations, nonlinear analysis and relations between symmetries and structural properties.

I recently investigated hierarchical structures, starting from group cohomology, continuing with semi-group theory and ending with lattices and universal algebra.

1d
comment Does a $\Pi_2^0$ sentence becomes equivalent to a $\Pi_1^0$ sentence after it has been proven?
Thanks for the long explanation. My real problems which are causing me not to understand are probably related to ordinal numbers and ordinal analysis. (However, I haven't mentioned those in the question, but apparently my explicit examples hinted at my problems.) Discussing PA as answer to my question certainly makes sense, because it is clear that I wonder about those connections. The main connection between ZFC and my question is that the consistency of ZFC is equivalent to a $\Pi_1^0$ sentence. Whether ZFC proves a certain well-order is irrelevant, because it might be inconsistent.
2d
comment Does a $\Pi_2^0$ sentence becomes equivalent to a $\Pi_1^0$ sentence after it has been proven?
@DavidC.Ullrich If that were true, then the answer to my question should be a resounding YES! But the example of Goodstein's theorem given in the question should make in clear that a $\Pi_2^0$ sentence can be true, without being equivalent to every other true sentence. (I actually hoped that Goodstein's theorem would be equivalent to (or at least imply) the consistency of PA, but I only found such a statement for the related Paris-Harrington theorem.) The case of the model existence theorem is more problematic, because it isn't really a statement about natural numbers.
May
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asked Does a $\Pi_2^0$ sentence becomes equivalent to a $\Pi_1^0$ sentence after it has been proven?
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awarded Tumbleweed
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awarded Necromancer
Apr
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answered ODEs vs DAE vs ADE?
Apr
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asked Is it reasonable to use B-splines to compute a radial symmetric electrostatic field?
Apr
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awarded Necromancer
Apr
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answered Real computers have only a finite number of states, so what is the relevance of Turing machines to real computers?
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revised Are QM interpretations physics or philosophy?
2 physics examples: Born rule in MWI, which QI need quantum gravity, 1 philosophy example: existence of worlds
Apr
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answered Are QM interpretations physics or philosophy?
Apr
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answered What are the major philosophical interpretations of probability?
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answered Community Promotion Ads - 2016
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answered How should one properly characterize mathematical conclusions?
Apr
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revised Which ontological commitments are embedded in a straightforward Turing machine model?
Asking a similar question on mathoverflow led to a much more definite (very technical) answer. Added explanations and links to that answer.
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answered What is the a fallacy that dismisses problems by presenting "bigger" problems?
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answered What is the relation between proof in mathematics and observation in physics?
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awarded Revival
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