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Peano axioms proof

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#proof-writing #peano-axioms
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Peano axioms proof attempt

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#solution-verification #peano-axioms
980
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Set of natural numbers and Peano axioms

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#natural-numbers #peano-axioms
74
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$\text{Sat}_{\Delta_0}(x, y)$ is $\Delta_1(\textbf{PA})$ (Kaye's book)

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#logic #model-theory #peano-axioms #nonstandard-models
149
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Prove that ever $\Sigma_0$ sentence is provable from PA (Peano Arithmetic, with exponentiation)

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#logic #peano-axioms #incompleteness
55
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Proving a result similar to the diagonal lemma/fixed-point theorem

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#logic #first-order-logic #predicate-logic #peano-axioms #incompleteness
30
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Proving $PAE ⊢ (Pr_S(\#(X → Y)) → (Pr_S(\#(X)) → Pr_S(\#(Y))))$, where $Pr_S(n)$ holds iff $n$ is the Gödel number of a formula provable from $S$

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#logic #first-order-logic #predicate-logic #peano-axioms #incompleteness
101
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Which is the axiom: well ordering principle, principle of induction, both, or none?

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#analysis #set-theory #peano-axioms
99
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Construction of the addition function

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#real-analysis #calculus #analysis #induction #peano-axioms
142
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prove $x+1 = 1+x$ using Peano axioms

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#induction #peano-axioms
64
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Motivation of indicator construction in Kaye

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#logic #model-theory #peano-axioms #nonstandard-models
143
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Set-up for the Paris-Harrington Theorem

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#logic #model-theory #peano-axioms #nonstandard-models
110
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Extension of the Paris-Harrington principle

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#combinatorics #logic #peano-axioms #nonstandard-models
97
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Are algebraic structures first order theories?

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#abstract-algebra #ring-theory #first-order-logic #model-theory #peano-axioms
180
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Nonlogical axioms and their validity

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#logic #first-order-logic #peano-axioms

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