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Proving incompleteness without unbound quantifiers

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#logic #incompleteness
73
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Enumerating axioms of PA in nonstandard models: trouble in the Kripke-Putnam proof of Gödel's incompleteness theorem

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#logic #incompleteness #nonstandard-models
117
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Gödel's Incompleteness Theorem - question

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#logic #incompleteness
86
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Is there a way to state the (in)completeness theorem for an arbitrary deductive system?

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#logic #incompleteness
707
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Is there a mathematical system that is: complete, consistent, and decidable?

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#incompleteness #modal-logic #meta-math
73
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Is incompleteness preserved by interpretations?

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#logic #model-theory #incompleteness
205
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Why do we care about PA proving itself consistent?

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#logic #first-order-logic #model-theory #incompleteness #nonstandard-models
74
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Are there any arithmetic statements where there does not exist a proof proving the statement?

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#peano-axioms #incompleteness
217
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Which sentences are irreducibly self-referential?

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#logic #proof-theory #peano-axioms #incompleteness
65
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Would a proof-search for a contradiction halt in non-standard models of PA arithmetic?

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#logic #first-order-logic #turing-machines #incompleteness
363
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Does this proof of Godel's incompleteness theorem rely on soundness?

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#logic #incompleteness #provability
75
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Can Peano arithmetic be completed using only atomic $\omega$-completions?

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#logic #proof-theory #incompleteness
84
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How are truth tables used in math?

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#logic #arithmetic #first-order-logic #incompleteness
172
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ZFC and Con(MK)

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#set-theory #model-theory #incompleteness
277
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Why was it important for Peano arithmetic to prove ITS OWN consistency?

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#logic #peano-axioms #incompleteness

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