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15
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Function which is weakly provably definable, but not provably definable

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#logic #peano-axioms
100
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I was able to "prove" by induction that $\forall n \in \mathbb{N} (n\geq 2 \implies n!>2^n)$. Where did I go wrong?

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#induction #fake-proofs #natural-numbers #peano-axioms
39
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Can I use a addition table with infinite length and height to define addition on the natural numbers rather than Peano's Axioms?

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#number-theory #arithmetic #natural-numbers #peano-axioms
39
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Peano categoricity is equivalent to weak konig lemma

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#logic #peano-axioms #second-order-logic #reverse-math
92
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What is the importance of Peano categoricity?

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#peano-axioms #second-order-logic #reverse-math
71
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non-constructive existence of a number

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#logic #first-order-logic #peano-axioms #formal-proofs
106
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Peano arithmetic without addition

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#arithmetic #peano-axioms
62
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Assuming the following definition of the addition of natural numbers, how do I prove that $\forall a:0+a=a$

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#proof-writing #induction #natural-numbers #peano-axioms
61
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Does Z₂ Prove the iteration theorem?

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#set-theory #peano-axioms #provability #second-order-logic #reverse-math
45
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In RCA0, Prove that for all n, fⁿ(i) exists

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#first-order-logic #peano-axioms #second-order-logic #reverse-math
59
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The set of all finite sequences in RCA0

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#peano-axioms #second-order-logic #reverse-math
56
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A Peano system with an infinite initial segment

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#logic #arithmetic #peano-axioms #second-order-logic #reverse-math
73
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Godelian sentences in other first order languages

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#first-order-logic #model-theory #foundations #peano-axioms #incompleteness
73
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What proof system is this paper by Hamano and Okada introducing?

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#logic #foundations #peano-axioms #formal-proofs
365
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How do I prove that the addition of natural numbers, as defined by Peano, is unique?

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#proof-writing #induction #first-order-logic #natural-numbers #peano-axioms

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