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unstableontology.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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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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xorshammer.com
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| | | | | We think of a proof as being non-constructive if it proves "There exists an $latex x$ such that $latex P(x)$ without ever actually exhibiting such an $latex x$. If you want to form a system of mathematics where all proofs are constructive, one thing you can do is remove the principle of proof by contradiction:... | |
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devyn.ca
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