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Interaction of completeness and second incompleteness theorems

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#reference-request #logic #incompleteness
902
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Con(PA) implies consistency of $\mathsf{PA}$ + ¬Con($\mathsf{PA}$)

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#logic #incompleteness #peano-axioms
306
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Does second-order arithmetic (Z2) prove soundness and uniform reflection for first-order arithmetic (PA)?

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#logic #proof-theory #incompleteness #higher-order-logic
178
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Peano's theory of arithmetic and Gödel's 1st Incompleteness Theorem

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#logic #model-theory #incompleteness
1.7k
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Must every decidable theory be axiomatizable?

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#logic #incompleteness
1.8k
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Modern book on Gödel's incompleteness theorems in all technical details

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#reference-request #logic #book-recommendation #incompleteness
623
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Gödel's incompleteness theorems: where to learn? Is there a straightforward relation between the two?

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#reference-request #logic #incompleteness
404
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If $T$ proves any incorrect $\forall$-rudimentary sentence, then $T$ is inconsistent

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#logic #first-order-logic #incompleteness #formal-systems
168
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Maths, esp. Godel, and poetry

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#formal-languages #incompleteness #turing-machines #meta-math
858
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Is Douglas Hofstadter's version of Godel's proof utter nonsense?

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#number-theory #logic #incompleteness
1.6k
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Why doesn't "$V$ is a model of $ZF$" imply consistency of ZF?

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#set-theory #incompleteness
812
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How did Kurt Gödel's Incompleteness Theorem affect the mathematical world?

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#math-history #incompleteness #big-picture
1.1k
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Concrete example for diagonal lemma

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#logic #incompleteness
2.4k
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Understanding ω-consistent and ω-incomplete theory

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#logic #incompleteness
374
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Scapegoat theory and PA

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#logic #incompleteness

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