Question

How to prove $x=5$ using the Peano Axioms?

score 111 · Answer 1 · 2026-03-26 16:05:32

How to prove $x=5$ using the Peano Axioms?

Published on 26 Mar 2026 - 16:05

score 105 · Answer 2 · 2020-03-19 02:14:59

"$\forall x$ s.t. $\phi(x), \exists y$ s.t $\phi'(x,y)$" versus "$\forall x, \big( \phi(x)\implies \exists y $ s.t $\phi'(x,y)\big)$"

score 33 · Answer 3 · 2020-03-19 20:45:36

33

Views

$\forall x \in S, \big( \phi(x) \rightarrow \phi'(x) \big)$ versus $\forall x , \big( \phi(x) \rightarrow \phi'(x) \big)$

Published on 19 Mar 2020 - 20:45

score 119 · Answer 4 · 2020-03-19 23:58:02

119

Views

What is "$\exists x \in S , \phi(x)$" shorthand for?

Published on 19 Mar 2020 - 23:58

score 55 · Answer 5 · 2026-03-25 13:51:02

55

Views

Predicate Logic - Equivalent Forms of Expression

Published on 25 Mar 2026 - 13:51

score 126 · Answer 6 · 2026-03-30 21:04:15

126

Views

Existence of a tower of conservative extensions of ZFC (as well as NBG)

Published on 30 Mar 2026 - 21:04

score 31 · Answer 7 · 2020-03-21 15:45:45

31

Views

Classification theory, forking, type: naming of a set of variables

Published on 21 Mar 2020 - 15:45

score 622 · Answer 8 · 2020-03-21 19:14:20

622

Views

First order logic for proving a prime number

Published on 21 Mar 2020 - 19:14

score 50 · Answer 9 · 2020-03-21 23:42:50

50

Views

Is the first order symbolic statement $\forall x (x \in M \land \phi(x) )$ always false?

Published on 21 Mar 2020 - 23:42

score 86 · Answer 10 · 2020-03-22 04:47:05

86

Views

How to formulate this lemma into a first order symbolic statement? (Finite Choice Lemma - Tao Analysis I)

Published on 22 Mar 2020 - 4:47

score 86 · Answer 11 · 2020-03-22 15:37:06

86

Views

Show $\Phi$ is true in a model $M$ if and only if ($\forall x$)$\Phi$ is true in $M$

Published on 22 Mar 2020 - 15:37

score 138 · Answer 12 · 2026-03-28 04:32:54

138

Views

Substituitions prove using structural induction

Published on 28 Mar 2026 - 4:32

score 136 · Answer 13 · 2020-03-23 15:37:40

136

Views

Uniqueness of first order logic representation

Published on 23 Mar 2020 - 15:37

score 212 · Answer 14 · 2020-03-24 19:55:05

212

Views

Negation with multiple quantifiers

Published on 24 Mar 2020 - 19:55

score 43 · Answer 15 · 2020-03-25 08:35:03

43

Views

Is there a definition of a translation from propositional logic to first order logic?

Published on 25 Mar 2020 - 8:35

List Question

How to prove $x=5$ using the Peano Axioms?

"$\forall x$ s.t. $\phi(x), \exists y$ s.t $\phi'(x,y)$" versus "$\forall x, \big( \phi(x)\implies \exists y $ s.t $\phi'(x,y)\big)$"

$\forall x \in S, \big( \phi(x) \rightarrow \phi'(x) \big)$ versus $\forall x , \big( \phi(x) \rightarrow \phi'(x) \big)$

What is "$\exists x \in S , \phi(x)$" shorthand for?

Predicate Logic - Equivalent Forms of Expression

Existence of a tower of conservative extensions of ZFC (as well as NBG)

Classification theory, forking, type: naming of a set of variables

First order logic for proving a prime number

Is the first order symbolic statement $\forall x (x \in M \land \phi(x) )$ always false?

How to formulate this lemma into a first order symbolic statement? (Finite Choice Lemma - Tao Analysis I)

Show $\Phi$ is true in a model $M$ if and only if ($\forall x$)$\Phi$ is true in $M$

Substituitions prove using structural induction

Uniqueness of first order logic representation

Negation with multiple quantifiers

Is there a definition of a translation from propositional logic to first order logic?

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