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Are these two definitions of the natural numbers equivalent?

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#natural-numbers #peano-axioms
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Model of Robinson Arithmetic but not Peano Arithmetic

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#logic #induction #model-theory #first-order-logic #peano-axioms
1.3k
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Non-standard models for Peano Axioms

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#peano-axioms #nonstandard-models
365
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Existence of nonstandard elementary extensions of $PA$?

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#logic #model-theory #peano-axioms #nonstandard-models
3.9k
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A question on Terence Tao's representation of Peano Axioms

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#real-analysis #peano-axioms
965
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Prove $n<m{++}\leq n{++}\iff m=n$ from Peano Axioms

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#peano-axioms
1.2k
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How can I prove this proposition from Peano Axioms?

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#peano-axioms
784
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Defining addition in second order logic

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#logic #arithmetic #peano-axioms #higher-order-logic
108
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Derive Peano Axioms from Properties of the Natural Numbers

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#reference-request #peano-axioms
129
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Theory of arithmetic equiconsistent with ZF

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#peano-axioms #meta-math
93
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How to define a large prime number (for example, $7919$)?

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#prime-numbers #definition #natural-numbers #peano-axioms
166
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Axiomatization of the naturals starting with the primes

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#prime-numbers #peano-axioms
73
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If the relation $f(x_1, ..., x_n)=y$ is $\Sigma_1$, then is its negation also $\Sigma_1$?

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#logic #recursion #computability #peano-axioms
174
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To what degree are arbitrary true statements about the natural numbers provable?

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#logic #first-order-logic #peano-axioms #incompleteness
94
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Proof involving Peano axiom

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#peano-axioms

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