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Why does incompleteness not imply consistency?

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#logic #foundations #incompleteness
370
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Existence of an inner model of ZFC implies $Con(ZFC)$?

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#logic #set-theory #foundations #incompleteness
413
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Gödel's second incompleteness theorems

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#logic #incompleteness
124
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Alternative approach in self-referential step of the proof of Gödel's first incompleteness theorem

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#logic #incompleteness
135
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Does Gödel's theorem rule out derivations from all possible logical systems or just first-order logic?

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#arithmetic #first-order-logic #incompleteness #peano-axioms
3.2k
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What's wrong with this "proof" that Gödel's first incompleteness theorem is wrong?

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#fake-proofs #incompleteness
138
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Are there "structure-specific" logical axiomatic systems? Do these have extra power?

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#logic #arithmetic #first-order-logic #incompleteness #peano-axioms
72
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"Un-coordinatable" Spaces

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#general-topology #geometry #incompleteness
438
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Is the set of primitive recursive functions (on $\mathbb{N}$) effectively enumerable?

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#computational-complexity #computability #recursion #incompleteness
36
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Supplementing $L_A$ with new function symbols

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#computational-complexity #computability #recursion #incompleteness
193
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Are statements of arithmetic without logical negation or existential quantifiers decidable?

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#logic #incompleteness #peano-axioms
3.4k
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With this definition of completeness, Gödel's Incompleteness result seems not surprising, so why it was back then?

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#logic #first-order-logic #incompleteness
113
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Categoricity of categorical arithmetic

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#arithmetic #incompleteness #peano-axioms #categorical-logic
416
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Is First Order Logic + Arithmetic semi-decidable?

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#discrete-mathematics #incompleteness #decidability
104
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How to understand Smullyan's notion of weakly adequate Gödel numbering

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#logic #incompleteness

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