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www.lesswrong.com | ||
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thehousecarpenter.wordpress.com
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| | | | | NB: I've opted to just get straight to the point with this post rather than attempting to introduce the subject first, so it may be of little interest to readers who aren't already interested in proving the completeness theorem for propositional logic. A PDF version of this document is available here. The key thing I... | |
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unstableontology.com
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| | | | | (note: one may find the embedded LaTeX more readable on LessWrong) The Löwenheim-Skolem theorem implies, among other things, that any first-order theory whose symbols are countable, and which has an infinite model, has a countably infinite model. This means that, in attempting to refer to uncountably infinite structures (such as in set theory), one "may... | |
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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. | |
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nationalinterest.org
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| | | It needs to be backed up by serious infrastructure investment. | ||
