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Prove if $x<y$ then $x+z<y+z$

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#induction #arithmetic #axioms #peano-axioms
534
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For each $x,y,z∈\mathbb N$, if $x<y$ then $x+z<y+z$

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#inequality #arithmetic #order-theory #peano-axioms
56
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For each $x,y∈\mathbb N$, if $x≤y$ and $y≤x$, then $x=y$

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#discrete-mathematics #arithmetic #order-theory #peano-axioms
173
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PA2 (Peano Arithmetic in 2º order logic and categoricty)

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#logic #peano-axioms
110
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Is $ConPA \rightarrow \neg \Box \neg ConPA$ true in the standard model of arithmetic?

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#logic #first-order-logic #peano-axioms
57
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End extension models of $I\Delta_0$

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#logic #model-theory #peano-axioms
169
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Why is there a need for ordinal analysis?

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#model-theory #peano-axioms
72
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A subtle point regarding the axiom of induction

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#elementary-number-theory #peano-axioms
1k
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Stuck on GEB chapter 9 - is b a MU number? is b a TNT number?

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#number-theory #logic #formal-languages #peano-axioms
509
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How do we know $\mathbb{N}$ is a model of Peano Arithmetic?

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#logic #model-theory #peano-axioms
106
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Peano Arithmetic: How would this formalized statement be correct?

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#logic #peano-axioms #formal-proofs #formal-systems
189
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Tao's definition of addition

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#peano-axioms
43
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Proving the artihmetic property of a theory

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#first-order-logic #peano-axioms
669
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Peano Arithmetic before Gödel

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#logic #math-history #peano-axioms
195
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On what sets other than $\mathbb{N}$ might we use proof by induction?

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#elementary-set-theory #logic #induction #peano-axioms

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