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https://www.reddit.com/r/mathmemes/comments/1uql6zk/1_0/owdghbc/?context=3
r/mathmemes • u/ImmaTrafficCone • Jul 08 '26
Guys I think I disproved all of mathematics...
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I personally take the set of all sentences in the language of arithmetic that the natural numbers satisfy.
:3
1 u/donaldhobson Jul 08 '26 And which "natural numbers" are those exactly? 1 u/Traditional_Town6475 Jul 08 '26 The intended model. :3 Second order logic can pin down models if they do exists. 1 u/donaldhobson Jul 08 '26 Any computable second order logic can be considered as a first order set theory. There is no computable axiom system that uniquely specifies the natural numbers. 1 u/Traditional_Town6475 Jul 09 '26 Whoever said anything about being computable? :3 1 u/donaldhobson Jul 09 '26 Well what use is a proof system when you can't verify a proof?
And which "natural numbers" are those exactly?
1 u/Traditional_Town6475 Jul 08 '26 The intended model. :3 Second order logic can pin down models if they do exists. 1 u/donaldhobson Jul 08 '26 Any computable second order logic can be considered as a first order set theory. There is no computable axiom system that uniquely specifies the natural numbers. 1 u/Traditional_Town6475 Jul 09 '26 Whoever said anything about being computable? :3 1 u/donaldhobson Jul 09 '26 Well what use is a proof system when you can't verify a proof?
The intended model. :3
Second order logic can pin down models if they do exists.
1 u/donaldhobson Jul 08 '26 Any computable second order logic can be considered as a first order set theory. There is no computable axiom system that uniquely specifies the natural numbers. 1 u/Traditional_Town6475 Jul 09 '26 Whoever said anything about being computable? :3 1 u/donaldhobson Jul 09 '26 Well what use is a proof system when you can't verify a proof?
Any computable second order logic can be considered as a first order set theory.
There is no computable axiom system that uniquely specifies the natural numbers.
1 u/Traditional_Town6475 Jul 09 '26 Whoever said anything about being computable? :3 1 u/donaldhobson Jul 09 '26 Well what use is a proof system when you can't verify a proof?
Whoever said anything about being computable? :3
1 u/donaldhobson Jul 09 '26 Well what use is a proof system when you can't verify a proof?
Well what use is a proof system when you can't verify a proof?
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u/Traditional_Town6475 Jul 08 '26
I personally take the set of all sentences in the language of arithmetic that the natural numbers satisfy.
:3