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carcinisation.com | ||
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www.logicmatters.net
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| | | | | A standard menu for a first mathematical logic course might be something like this: (1) A treatment of the syntax and semantics of FOL, presenting a proof system or two, leading up to a proof of a Gödel's completeness theorem (and then a glance at e.g. the compactness theorem and some initial implications). (2) An [...] | |
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dvt.name
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| | | | | Gödel's incompleteness theorems have been hailed as "the greatest mathematical discoveries of the 20th century" - indeed, the theorems apply not only to mathematics, but all formal systems and have deep implications for science, logic, computer science, philosophy, and so on. In this post, I'll give a simple but rigorous sketch of Gödel's First Incompleteness ... | |
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www.logicmatters.net
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| | | | | I didn't at all intend to return to my Introduction to Gödel's Theorems (which I've not really read for a dozen years, apart from correcting a small handful of typos in the PDF). But I had occasion to look something up, and - hey, ho! - I've found myself over the last week beginning to [...] | |
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blog.sigfpe.com
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| | | [AI summary] The article explains why defining a truth predicate for set theory (ZF) is impossible despite the success of similar definitions in propositional calculus and Peano arithmetic, based on Tarski's theorem and the limitations of transfinite recursion when applied to infinite collections of children. | ||
