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How valid are the statements of ZFC being consistent up to very extreme ordinals?

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#set-theory #ordinals #incompleteness
102
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Gödel's second incompleteness theorem and Consistency.

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#logic #axioms #peano-axioms #incompleteness
92
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Can Gödel's theorem be proved within PA?

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#logic #proof-theory #incompleteness
244
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Gödel on the “True Reason” for Incompleteness

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#logic #math-history #incompleteness #type-theory #formal-systems
104
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"Proof" that "ZFC + there exists an inaccessible cardinal" is consistent

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#set-theory #cardinals #incompleteness #large-cardinals
98
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Are there Nonstandard Models of Arithmetic that don't Add Additional Axioms?

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#first-order-logic #model-theory #peano-axioms #incompleteness
61
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Is Robinson arithmetic the weakest incompletable system of arithmetic?

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#logic #incompleteness
395
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How do mathematicians know if they are extending the theory of natural numbers in the right direction?

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#soft-question #set-theory #foundations #natural-numbers #incompleteness
49
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Negation completeness and maximally consistent

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#logic #first-order-logic #incompleteness
83
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Is the sublanguage immune from Gödel theorem

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#logic #arithmetic #computability #turing-machines #incompleteness
169
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Prove the Gödel theorem using the Busy Beaver function

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#logic #arithmetic #computability #turing-machines #incompleteness
51
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How to prove the Gödel sentence is true (in the metalanguage), assuming only consistency of a theory.

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#first-order-logic #incompleteness #metalogic
65
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Gödel's incompleteness theorems for soundness or semantic consistency

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#logic #turing-machines #incompleteness
35
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Gödel's first incompleteness theorem from halting problem using soundness. Is it possible to use semantic consistency?

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#logic #turing-machines #incompleteness
88
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Are there "Godel encodings" for non-arithmetic theories?

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#logic #arithmetic #incompleteness #metalogic

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