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xorshammer.com | ||
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jdh.hamkins.org
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| | | | | I'd like to share a simple proof I've discovered recently of a surprising fact: there is a universal algorithm, capable of computing any given function! Wait, what? What on earth do I ... | |
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billwadge.com
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| | | | | The famous mathematician Kurt Gödel proved two "incompleteness" theorems. This is their story. By the 1930s logicians, especially Tarski, had figured out the semantics of predicate logic. Tarski described what exactly was an 'interpretation' and what it meant for a formula to be true in an interpretation. Briefly, an interpretation is a nonempty set (the... | |
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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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ianwrightsite.wordpress.com
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| | | Are Cantor's higher infinities really real? | ||