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Goodstein's theorem is easily provable in the [Dedekind 1888] theory of the Natural Numbers. Cohen's incompleteness results do not hold for a theory of sets th
by ProfHewitt 7y ago
Goodstein's theorem is easily provable in the [Dedekind 1888] theory of the Natural Numbers.
Cohen's incompleteness results do not hold for a theory of sets that axiomatizes sets up to a unique isomorphism. See the following:
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3457802 https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3457802
- cscurmudgeon 7y agoBut the thing is you are just trading off computability. Aren't you? > The theory Ordinals is algorithmically inexhaustible
- ProfHewitt 7y agoExcellent question! Proof checking in the theory Ordinals is algorithmically checkable although theorems are not computationally enumerable because instances of strongly-typed induction axiom are uncountable.
- cscurmudgeon 7y agoThank you! Can't believe I had a conversation with Prof. Carl Hewitt here! Love the actor calculus btw!
- ProfHewitt 7y agoYou are very welcome! Cheers, Carl
- a1369209993 7y agoCould you provide a direct link to that paper? The PDF link at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3457802 https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3457802 ( https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID3488706_code2561841.pdf?abstractid=3457802&mirid=1 https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID3488706_cod... ) is broken ( 302 redirects back to https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3457802 https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3457802 ).
- ProfHewitt 7y agoWhat browser are you using? The link below works for me in FireFox: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3457802 https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3457802
- a1369209993 7y agoGNU Wget 1.20.1 built on linux-gnu. That URL produces a HTML page containing a link to "Delivery.cfm/SSRN_ID3488706_code2561841.pdf?abstractid=3457802&mirid=1" with text "Download This Paper", which I assume is supposed to be the direct link. However https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID3488706_code2561841.pdf?abstractid=3457802&mirid=1 https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID3488706_cod... 302 redirects back to https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3457802 https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3457802 .
- ProfHewitt 7y agoThe following link also works for me in Chrome on Windows: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3457802 https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3457802
- a1369209993 7y agoThat is the same link. It produces a HTML page containing a abstract of the paper (not the paper itself) and a link that purports to be to the full paper, but actually 302 redirects back your (abstract) link.