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Predicate logic equivalence

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#logic #first-order-logic #incompleteness
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Consistent theories $T$ such that $T+\mathrm{Con}(T+\mathrm{Con}(T))$ is inconsistent

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#logic #incompleteness #provability #nonstandard-models
135
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Circularity in the argument that Gödel's incompleteness theorems undermine Hilbert's program

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#logic #formal-languages #incompleteness #formal-proofs #formal-systems
271
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Is there a theory stronger than ZFC in consistency but does not prove its consistency?

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#logic #set-theory #incompleteness
33
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Can a second-order theory that contains the first-order theory of the structure (N,+,x,1) have a decidable axiomatization?

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#incompleteness
108
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is arithmetic finitely consistent?

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#proof-explanation #first-order-logic #peano-axioms #incompleteness
138
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Infinite statements from finite axioms

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#proof-explanation #first-order-logic #peano-axioms #incompleteness
95
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Confusion about $\mathsf{PA}$'s self-provable consistency sentences

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#logic #foundations #peano-axioms #incompleteness
33
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Need help understanding Godel's incompleteness Theorem Proof

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#incompleteness
158
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Precise statement of Gödel's Incompleteness Theorems

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#logic #peano-axioms #incompleteness
53
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Decoding Gödel's number inside Gödel's number

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#logic #incompleteness #formal-systems
94
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Does Peano's axioms axiomize true arithmetic?

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#logic #model-theory #incompleteness
404
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PA + "(PA + this axiom) is consistent"

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#logic #axioms #peano-axioms #incompleteness
121
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Is Gödels second incompleteness theorem provable within peano arithmetic?

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#logic #solution-verification #peano-axioms #incompleteness #provability
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How to prove that Gödel's Incompleteness Theorems apply to ZFC?

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#logic #set-theory #predicate-logic #first-order-logic #incompleteness

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