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Is truth outrunning provability equivalent to undecidability of some statement in a theory?

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#logic #first-order-logic #incompleteness
90
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Is the function sending a sentence to the diagonal of a sentence form extended over it, computable?

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#logic #first-order-logic #computability #incompleteness
91
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Gödels incompleteness theorem false for natural numbers

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#peano-axioms #incompleteness #nonstandard-models
107
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Is someone trying to solve problems by building all possible proofs using all possible rules of inference?

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#turing-machines #incompleteness #provability #automated-theorem-proving
114
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About Gödel's completeness and incompleteness theorems

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#computability #incompleteness
94
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Does inconsistency imply incompleteness?

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#logic #incompleteness
177
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Why Godel have chosen $\omega$-consistency of a theory instead of it proving it's own consistency?

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#logic #first-order-logic #incompleteness
138
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Confusion about the consistency of $\mathsf{ZFC}+\neg\mathsf{Con}(\mathsf{ZFC})$

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#logic #first-order-logic #incompleteness
166
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Gödel’s Incompleteness Theorems Simple Wikipedia

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#logic #solution-verification #incompleteness
81
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Gödel's theorems, Löb's theorem, difference between "proves" and "implies"

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#propositional-calculus #incompleteness #metalogic
195
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meaning of ɷ-consistency......

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#logic #set-theory #incompleteness
78
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What is decidability and completeness?

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#logic #incompleteness #decidability
112
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Is there a sequence $\mathbb{N}^*\to\mathbb{N}^*$, not depending on the model of $\mathsf{ZFC}$, whose convergence is independent of $\mathsf{ZFC}$?

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#logic #set-theory #incompleteness
86
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What are the consequences of negating the Godel sentence in a formal system?

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#logic #incompleteness
1k
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In his 1931 incompleteness proof, how does Godel's definition of "immediate consequence" work?

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#logic #first-order-logic #incompleteness

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