Oratory
发表于 2025-3-23 09:56:10
Der Rundfunk und der Weltfunkvertrag,The ultraproduct construction is introduced and used to give an alternative proof of the Compactness Theorem.
hermetic
发表于 2025-3-23 14:28:37
Die Londoner Funkkonferenz 1912,A test for eliminating quantifiers is given and applied it to further study the model theory of algebraically closed fields.
消息灵通
发表于 2025-3-23 21:21:55
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Opponent
发表于 2025-3-23 23:35:13
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GEON
发表于 2025-3-24 03:54:04
https://doi.org/10.1007/978-3-642-10271-4Turing’s universal machine is constructed and used to prove the undecidability of the Halting Problem and the undecidability of validity in first-order logic. We include a brief discussion of the Recursion Theorem.
placebo-effect
发表于 2025-3-24 09:07:46
https://doi.org/10.1007/978-3-642-10271-4We introduce the computably enumerable sets and the arithmetic sets and show that the form a hierarchy. These results, and the existence of computably inseparable computably enumerably sets, will be used in our approach to the Incompleteness Theorem. We briefly study Kolmogorov randomness as another avatar of incompleteness phenomena.
Decimate
发表于 2025-3-24 12:11:49
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伪书
发表于 2025-3-24 15:41:01
https://doi.org/10.1007/978-3-642-10271-4Gödel’s Incompleteness Theorems are proved. We show that the sets definable in the natural numbers are exactly the arithmetic sets. The Arithmetized Completeness Theorem is used to give an alternative proof of the Second Incompleteness Theorem.
转向
发表于 2025-3-24 19:55:06
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掺假
发表于 2025-3-25 00:47:12
,Fünfter Teil: Thesen der Arbeit,We bound the growth rate of computable functions provably total in Peano Arithmetic. This is applied to show the independence of Goodstein’s number theoretic result. Proof theoretic methods, including cut-elimination, are introduced to prove the main result.