Question

Proving $a\ne{b}\implies{a<b}\lor{b<a}$ for natural numbers beginning with 1 using Peano's Axioms without induction hypothesis

score 246 · Answer 1 · 2019-03-30 23:18:29

246

Views

Proving $a\ne{b}\implies{a<b}\lor{b<a}$ for natural numbers beginning with 1 using Peano's Axioms without induction hypothesis

Published on 30 Mar 2019 - 23:18

score 1.2k · Answer 2 · 2019-03-31 00:23:48

1.2k

Views

Peano axioms and commutativity of addition

Published on 31 Mar 2019 - 0:23

score 190 · Answer 3 · 2019-03-31 23:20:53

190

Views

First Order Logic Peano arithmetic Proof

Published on 31 Mar 2019 - 23:20

score 96 · Answer 4 · 2019-04-04 04:08:27

96

Views

What is the pitfall in the inductive "proof" of P(x):= x does not succeed 1?

Published on 04 Apr 2019 - 4:08

score 645 · Answer 5 · 2026-03-25 09:23:24

645

Views

Consistent theories that proves their own consistence

Published on 25 Mar 2026 - 9:23

score 640 · Answer 6 · 2019-04-16 15:28:00

640

Views

In Peano's Axioms are the uniqueness of the successor and $x^{\prime}=y^{\prime}\implies{x=y}$ redundant?

Published on 16 Apr 2019 - 15:28

score 129 · Answer 7 · 2026-02-23 02:56:52

129

Views

Decidability of Gödel sentences.

Published on 23 Feb 2026 - 2:56

score 60 · Answer 8 · 2019-04-24 15:51:42

60

Views

Is there a formal term for the algebraic structure equivalent to Thurston's hemigroup without identity?

Published on 24 Apr 2019 - 15:51

score 624 · Answer 9 · 2019-04-24 21:08:04

624

Views

Can we prove the Peano axioms from a type theoretic construction of the natural numbers?

Published on 24 Apr 2019 - 21:08

score 126 · Answer 10 · 2026-03-25 04:22:24

126

Views

First-order Peano arithmetic and (the lack of) implicit definition of addition

Published on 25 Mar 2026 - 4:22

score 48 · Answer 11 · 2019-04-28 02:01:51

48

Views

Is this a valid proof that $\forall_{x,y}\left[x\ne y\implies x<y\lor x>y\right]$ in $\mathbb{N}_1$?

Published on 28 Apr 2019 - 2:01

score 321 · Answer 12 · 2019-04-28 04:17:25

321

Views

How would I show that PA proves the godel sentence for PA implies Con(PA)

Published on 28 Apr 2019 - 4:17

score 82 · Answer 13 · 2019-04-28 05:21:43

82

Views

How is it shown using the additive cancellation law that $x\mapsto x+h$ has an inverse?

Published on 28 Apr 2019 - 5:21

score 262 · Answer 14 · 2019-04-29 08:21:05

262

Views

In the extension to integers, how should this restriction on the domain of natural numbers be interpreted?

Published on 29 Apr 2019 - 8:21

score 167 · Answer 15 · 2026-03-25 06:21:16

167

Views

Is it consistent for $P(\mathbb{N})$ to be present in a low layer of the Constructible Universe?

Published on 25 Mar 2026 - 6:21

List Question

Proving $a\ne{b}\implies{a<b}\lor{b<a}$ for natural numbers beginning with 1 using Peano's Axioms without induction hypothesis

Peano axioms and commutativity of addition

First Order Logic Peano arithmetic Proof

What is the pitfall in the inductive "proof" of P(x):= x does not succeed 1?

Consistent theories that proves their own consistence

In Peano's Axioms are the uniqueness of the successor and $x^{\prime}=y^{\prime}\implies{x=y}$ redundant?

Decidability of Gödel sentences.

Is there a formal term for the algebraic structure equivalent to Thurston's hemigroup without identity?

Can we prove the Peano axioms from a type theoretic construction of the natural numbers?

First-order Peano arithmetic and (the lack of) implicit definition of addition

Is this a valid proof that $\forall_{x,y}\left[x\ne y\implies x<y\lor x>y\right]$ in $\mathbb{N}_1$?

How would I show that PA proves the godel sentence for PA implies Con(PA)

How is it shown using the additive cancellation law that $x\mapsto x+h$ has an inverse?

In the extension to integers, how should this restriction on the domain of natural numbers be interpreted?

Is it consistent for $P(\mathbb{N})$ to be present in a low layer of the Constructible Universe?

Trending Questions

Popular # Hahtags

Popular Questions