List questions from peano-axioms

Published on 27 Mar 2018 - 14:50

92

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Equivalence of $I\Sigma_n$ and $I\Pi_n$

Published on 25 Mar 2026 - 4:40

70

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$(m \not \mid n \wedge m \neq 0) \Leftrightarrow (\exists p, 0<q<m \text{ s.t } n=pm+q)$ [Proof Verification]

Published on 29 Mar 2018 - 6:57

89

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$a < b$ iff $S(a) \leq b$

Published on 24 Mar 2026 - 23:42

632

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Is my proof correct that $a < b \implies S(a) \leq b$?

Published on 30 Mar 2018 - 19:49

110

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Proving that for $x \neq 0$ there exists a $y$ such that $S(y) = x$.

Published on 31 Mar 2018 - 15:57

119

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How much of first order statements can we derive purely from the definitions in arithmetic?

Published on 23 Mar 2026 - 3:56

135

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Does Gödel's theorem rule out derivations from all possible logical systems or just first-order logic?

Published on 24 Mar 2026 - 22:09

138

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Are there "structure-specific" logical axiomatic systems? Do these have extra power?

Published on 24 Mar 2026 - 22:08

1.7k

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Let $a$ be a positive number. Then there exists exactly one natural number $b$ such that $b\text{++} =a$.

Published on 01 Apr 2018 - 19:53

193

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Are statements of arithmetic without logical negation or existential quantifiers decidable?

Published on 24 Mar 2026 - 22:08

56

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Limit case of PA theories?

Published on 21 Mar 2026 - 23:58

113

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Categoricity of categorical arithmetic

Published on 22 Mar 2026 - 21:53

179

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Is the set of bounded quantified sentences decidable in PA

Published on 15 Apr 2018 - 22:01

74

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Strongest decidable system of arithmetics

Published on 23 Mar 2026 - 10:19

List Question

$\forall n \in \mathbb{N}, n$ is even $\Leftrightarrow n+1$ is odd

Equivalence of $I\Sigma_n$ and $I\Pi_n$

$(m \not \mid n \wedge m \neq 0) \Leftrightarrow (\exists p, 0<q<m \text{ s.t } n=pm+q)$ [Proof Verification]

$a < b$ iff $S(a) \leq b$

Is my proof correct that $a < b \implies S(a) \leq b$?

Proving that for $x \neq 0$ there exists a $y$ such that $S(y) = x$.

How much of first order statements can we derive purely from the definitions in arithmetic?

Does Gödel's theorem rule out derivations from all possible logical systems or just first-order logic?

Are there "structure-specific" logical axiomatic systems? Do these have extra power?

Let $a$ be a positive number. Then there exists exactly one natural number $b$ such that $b\text{++} =a$.

Are statements of arithmetic without logical negation or existential quantifiers decidable?

Limit case of PA theories?

Categoricity of categorical arithmetic

Is the set of bounded quantified sentences decidable in PA

Strongest decidable system of arithmetics

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