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Proving fundamental theorem of arithmetic using primitive recursive functions

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#logic #incompleteness
256
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Why Godel's theorem influences Hilbert's programme?

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#logic #incompleteness
274
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Reference textbook for Godel's incompleteness theorems proved in PRA or PA metatheory

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#logic #reference-request #incompleteness
42
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Can the Incompleteness Theorems be proven in the context of other logics, for example with Paraconsistent Logic?

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#logic #incompleteness
277
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Gödel's incompleteness 1: construction of the formula relating Gödel number of proof to Gödel number of proven statement

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#logic #first-order-logic #incompleteness
2.8k
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Why can't we prove consistency of ZFC like we can for PA?

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#logic #set-theory #model-theory #incompleteness
195
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Why is $\forall x (x = x)$ an example of a first order sentence that is neither provable nor disprovable?

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#first-order-logic #incompleteness
113
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Recursion Theory/Incompleteness Theorems: Computability of sets of formulas in first order logic

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#logic #first-order-logic #computability #incompleteness #decidability
1.2k
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Gödel's completeness theorem and the undecidability of first-order logic

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#logic #first-order-logic #computability #incompleteness #decidability
940
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How can a formal system ever be non-obviously unsound?

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#logic #model-theory #incompleteness
2.5k
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Example of incomplete, but decidable theory, and of complete and undecidable theory, question

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#logic #first-order-logic #computability #incompleteness #decidability
74
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Is every theory meeting Gödels incompleteness, also incomplete below its consistency level?

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#first-order-logic #incompleteness
135
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Why the 'natural' consistency proof of PA cannot be carried out $\textbf{in}$ PA

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#foundations #proof-theory #incompleteness #meta-math #provability
229
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An alternative formulation (or corollary) of Tarski's theorem? [Or just a typo?]

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#logic #proof-theory #incompleteness #meta-math #provability
249
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Are the HBL derivability conditions necessary for Gödel's incompleteness theorems? (For Löb's theorem?)

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#logic #proof-theory #incompleteness #meta-math #provability

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