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daniellefong.com | ||
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www.logicmatters.net
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| | | | | Quick links Download PDF of An Introduction to Gödel's Theorems. Download PDF of Gödel Without (Too Many) Tears. The big book An Introduction to Gödel's Theorems was first published by CUP in 2007 with the second edition appearing in 2013. A corrected version of the second edition is nowavailable as a freely downloadable PDF. Many [...] | |
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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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dvt.name
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| | | | | In the previous blog post in this series, we looked at Gödel's First Incompleteness Theorem, and came to the amazing conclusion that we can't compute certain kinds of functions in formal systems (like Javascript). Specifically, we looked at a special function, , which turned out to be non-computable. In case we forgot, the first incompleteness ... | |
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www.jeremykun.com
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| | | This proof assumes knowledge of complex analysis, specifically the notions of analytic functions and Liouville's Theorem (which we will state below). The fundamental theorem of algebra has quite a few number of proofs (enough to fill a book!). In fact, it seems a new tool in mathematics can prove its worth by being able to prove the fundamental theorem in a different way. This series of proofs of the fundamental theorem also highlights how in mathematics there are many many ways to prove a single theorem... | ||
