proof that weak axiom of pairing and axiom schema of specification imply axiom of pairing
$begingroup$
as the title says I am trying to give a (nearly, but not fully formal) proof that the weak axiom of pairing (i.e. $forall x forall y exists p: x in p wedge y in p$) together with a suitable instance of the axiom schema of specification does imply the axiom of pairing.
I haven't found a suitable instance yet, so this would be the first step to take.
elementary-set-theory logic proof-writing axioms
edited Jan 12 at 21:16
Andrés E. Caicedo
65.2k8158247
asked Jan 12 at 17:34
StudentuStudentu
1228
$endgroup$
add a comment |
$begingroup$
as the title says I am trying to give a (nearly, but not fully formal) proof that the weak axiom of pairing (i.e. $forall x forall y exists p: x in p wedge y in p$) together with a suitable instance of the axiom schema of specification does imply the axiom of pairing.
I haven't found a suitable instance yet, so this would be the first step to take.
elementary-set-theory logic proof-writing axioms
edited Jan 12 at 21:16
Andrés E. Caicedo
65.2k8158247
asked Jan 12 at 17:34
StudentuStudentu
1228
$endgroup$
add a comment |
$begingroup$
as the title says I am trying to give a (nearly, but not fully formal) proof that the weak axiom of pairing (i.e. $forall x forall y exists p: x in p wedge y in p$) together with a suitable instance of the axiom schema of specification does imply the axiom of pairing.
I haven't found a suitable instance yet, so this would be the first step to take.
elementary-set-theory logic proof-writing axioms
edited Jan 12 at 21:16
Andrés E. Caicedo
65.2k8158247
asked Jan 12 at 17:34
StudentuStudentu
1228
$endgroup$
as the title says I am trying to give a (nearly, but not fully formal) proof that the weak axiom of pairing (i.e. $forall x forall y exists p: x in p wedge y in p$) together with a suitable instance of the axiom schema of specification does imply the axiom of pairing.
I haven't found a suitable instance yet, so this would be the first step to take.
elementary-set-theory logic proof-writing axioms
elementary-set-theory logic proof-writing axioms
edited Jan 12 at 21:16
Andrés E. Caicedo
65.2k8158247
asked Jan 12 at 17:34
StudentuStudentu
1228
edited Jan 12 at 21:16
Andrés E. Caicedo
65.2k8158247
asked Jan 12 at 17:34
StudentuStudentu
1228
edited Jan 12 at 21:16
Andrés E. Caicedo
65.2k8158247
edited Jan 12 at 21:16
Andrés E. Caicedo
65.2k8158247
edited Jan 12 at 21:16
Andrés E. Caicedo
65.2k8158247
65.2k8158247
asked Jan 12 at 17:34
StudentuStudentu
1228
asked Jan 12 at 17:34
StudentuStudentu
1228
asked Jan 12 at 17:34
StudentuStudentu
1228
1228
add a comment |
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
Here is a 'nearly, but not fully, formal proof' (OK, it is fully formal, but it is not fully completed):
answered Jan 12 at 18:42
Bram28Bram28
61.4k44792
$endgroup$
1
$begingroup$
What software is that?
$endgroup$
– J.G.
Jan 12 at 18:46
1
$begingroup$
@J.G. It's called 'Fitch' .. it comes with the book "Language, Proof, and Logic"
$endgroup$
– Bram28
Jan 12 at 19:14
$begingroup$
This software seems awesome! (Though I don't fully understand the notions there.) Thank you for your reply!
$endgroup$
– Studentu
Jan 13 at 18:10
1
$begingroup$
@Studentu The 'Fitch' system is actually a fairly well known and well-used system for creating fully formal proofs. Here is a list with all the rules: math.mcgill.ca/rags/JAC/124/Rules-Strategy-b.pdf
$endgroup$
– Bram28
Jan 13 at 18:21
1
$begingroup$
@Studentu Cool. You're welcome! :)
$endgroup$
– Bram28
Jan 15 at 1:31
|
show 1 more comment
$begingroup$
Given $x,y$, let $p$ be such that $xin pland yin p$. Then ${x,y}={,tin pmid t=xlor t=y,}$.
answered Jan 12 at 17:37
Hagen von EitzenHagen von Eitzen
278k22269498
$endgroup$
$begingroup$
Thanks for your answer!
$endgroup$
– Studentu
Jan 13 at 18:09
add a comment |
$begingroup$
Fix $x,y$ and take $p$ such that $x, y in p$. Now take the formula $Phi = ( z = x lor z = y)$ and apply the axiom of specification on $p$.
answered Jan 12 at 17:40
Lucas HenriqueLucas Henrique
1,032414
$endgroup$
$begingroup$
Thank you for answering!
$endgroup$
– Studentu
Jan 13 at 18:09
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Here is a 'nearly, but not fully, formal proof' (OK, it is fully formal, but it is not fully completed):
answered Jan 12 at 18:42
Bram28Bram28
61.4k44792
$endgroup$
1
$begingroup$
What software is that?
$endgroup$
– J.G.
Jan 12 at 18:46
1
$begingroup$
@J.G. It's called 'Fitch' .. it comes with the book "Language, Proof, and Logic"
$endgroup$
– Bram28
Jan 12 at 19:14
$begingroup$
This software seems awesome! (Though I don't fully understand the notions there.) Thank you for your reply!
$endgroup$
– Studentu
Jan 13 at 18:10
1
$begingroup$
@Studentu The 'Fitch' system is actually a fairly well known and well-used system for creating fully formal proofs. Here is a list with all the rules: math.mcgill.ca/rags/JAC/124/Rules-Strategy-b.pdf
$endgroup$
– Bram28
Jan 13 at 18:21
1
$begingroup$
@Studentu Cool. You're welcome! :)
$endgroup$
– Bram28
Jan 15 at 1:31
|
show 1 more comment
$begingroup$
Here is a 'nearly, but not fully, formal proof' (OK, it is fully formal, but it is not fully completed):
answered Jan 12 at 18:42
Bram28Bram28
61.4k44792
$endgroup$
1
$begingroup$
What software is that?
$endgroup$
– J.G.
Jan 12 at 18:46
1
$begingroup$
@J.G. It's called 'Fitch' .. it comes with the book "Language, Proof, and Logic"
$endgroup$
– Bram28
Jan 12 at 19:14
$begingroup$
This software seems awesome! (Though I don't fully understand the notions there.) Thank you for your reply!
$endgroup$
– Studentu
Jan 13 at 18:10
1
$begingroup$
@Studentu The 'Fitch' system is actually a fairly well known and well-used system for creating fully formal proofs. Here is a list with all the rules: math.mcgill.ca/rags/JAC/124/Rules-Strategy-b.pdf
$endgroup$
– Bram28
Jan 13 at 18:21
1
$begingroup$
@Studentu Cool. You're welcome! :)
$endgroup$
– Bram28
Jan 15 at 1:31
|
show 1 more comment
$begingroup$
Here is a 'nearly, but not fully, formal proof' (OK, it is fully formal, but it is not fully completed):
answered Jan 12 at 18:42
Bram28Bram28
61.4k44792
$endgroup$
Here is a 'nearly, but not fully, formal proof' (OK, it is fully formal, but it is not fully completed):
answered Jan 12 at 18:42
Bram28Bram28
61.4k44792
edited Jan 12 at 19:18
answered Jan 12 at 18:42
Bram28Bram28
61.4k44792
answered Jan 12 at 18:42
Bram28Bram28
61.4k44792
answered Jan 12 at 18:42
Bram28Bram28
61.4k44792
61.4k44792
1
$begingroup$
What software is that?
$endgroup$
– J.G.
Jan 12 at 18:46
1
$begingroup$
@J.G. It's called 'Fitch' .. it comes with the book "Language, Proof, and Logic"
$endgroup$
– Bram28
Jan 12 at 19:14
$begingroup$
This software seems awesome! (Though I don't fully understand the notions there.) Thank you for your reply!
$endgroup$
– Studentu
Jan 13 at 18:10
1
$begingroup$
@Studentu The 'Fitch' system is actually a fairly well known and well-used system for creating fully formal proofs. Here is a list with all the rules: math.mcgill.ca/rags/JAC/124/Rules-Strategy-b.pdf
$endgroup$
– Bram28
Jan 13 at 18:21
1
$begingroup$
@Studentu Cool. You're welcome! :)
$endgroup$
– Bram28
Jan 15 at 1:31
|
show 1 more comment
1
$begingroup$
What software is that?
$endgroup$
– J.G.
Jan 12 at 18:46
1
$begingroup$
@J.G. It's called 'Fitch' .. it comes with the book "Language, Proof, and Logic"
$endgroup$
– Bram28
Jan 12 at 19:14
$begingroup$
This software seems awesome! (Though I don't fully understand the notions there.) Thank you for your reply!
$endgroup$
– Studentu
Jan 13 at 18:10
1
$begingroup$
@Studentu The 'Fitch' system is actually a fairly well known and well-used system for creating fully formal proofs. Here is a list with all the rules: math.mcgill.ca/rags/JAC/124/Rules-Strategy-b.pdf
$endgroup$
– Bram28
Jan 13 at 18:21
1
$begingroup$
@Studentu Cool. You're welcome! :)
$endgroup$
– Bram28
Jan 15 at 1:31
1
1
$begingroup$
What software is that?
$endgroup$
– J.G.
Jan 12 at 18:46
$begingroup$
What software is that?
$endgroup$
– J.G.
Jan 12 at 18:46
1
1
$begingroup$
@J.G. It's called 'Fitch' .. it comes with the book "Language, Proof, and Logic"
$endgroup$
– Bram28
Jan 12 at 19:14
$begingroup$
@J.G. It's called 'Fitch' .. it comes with the book "Language, Proof, and Logic"
$endgroup$
– Bram28
Jan 12 at 19:14
$begingroup$
This software seems awesome! (Though I don't fully understand the notions there.) Thank you for your reply!
$endgroup$
– Studentu
Jan 13 at 18:10
$begingroup$
This software seems awesome! (Though I don't fully understand the notions there.) Thank you for your reply!
$endgroup$
– Studentu
Jan 13 at 18:10
1
1
$begingroup$
@Studentu The 'Fitch' system is actually a fairly well known and well-used system for creating fully formal proofs. Here is a list with all the rules: math.mcgill.ca/rags/JAC/124/Rules-Strategy-b.pdf
$endgroup$
– Bram28
Jan 13 at 18:21
$begingroup$
@Studentu The 'Fitch' system is actually a fairly well known and well-used system for creating fully formal proofs. Here is a list with all the rules: math.mcgill.ca/rags/JAC/124/Rules-Strategy-b.pdf
$endgroup$
– Bram28
Jan 13 at 18:21
1
1
$begingroup$
@Studentu Cool. You're welcome! :)
$endgroup$
– Bram28
Jan 15 at 1:31
$begingroup$
@Studentu Cool. You're welcome! :)
$endgroup$
– Bram28
Jan 15 at 1:31
|
show 1 more comment
$begingroup$
Given $x,y$, let $p$ be such that $xin pland yin p$. Then ${x,y}={,tin pmid t=xlor t=y,}$.
answered Jan 12 at 17:37
Hagen von EitzenHagen von Eitzen
278k22269498
$endgroup$
$begingroup$
Thanks for your answer!
$endgroup$
– Studentu
Jan 13 at 18:09
add a comment |
$begingroup$
Given $x,y$, let $p$ be such that $xin pland yin p$. Then ${x,y}={,tin pmid t=xlor t=y,}$.
answered Jan 12 at 17:37
Hagen von EitzenHagen von Eitzen
278k22269498
$endgroup$
$begingroup$
Thanks for your answer!
$endgroup$
– Studentu
Jan 13 at 18:09
add a comment |
$begingroup$
Given $x,y$, let $p$ be such that $xin pland yin p$. Then ${x,y}={,tin pmid t=xlor t=y,}$.
answered Jan 12 at 17:37
Hagen von EitzenHagen von Eitzen
278k22269498
$endgroup$
Given $x,y$, let $p$ be such that $xin pland yin p$. Then ${x,y}={,tin pmid t=xlor t=y,}$.
answered Jan 12 at 17:37
Hagen von EitzenHagen von Eitzen
278k22269498
answered Jan 12 at 17:37
Hagen von EitzenHagen von Eitzen
278k22269498
answered Jan 12 at 17:37
Hagen von EitzenHagen von Eitzen
278k22269498
answered Jan 12 at 17:37
Hagen von EitzenHagen von Eitzen
278k22269498
278k22269498
$begingroup$
Thanks for your answer!
$endgroup$
– Studentu
Jan 13 at 18:09
add a comment |
$begingroup$
Thanks for your answer!
$endgroup$
– Studentu
Jan 13 at 18:09
$begingroup$
Thanks for your answer!
$endgroup$
– Studentu
Jan 13 at 18:09
$begingroup$
Thanks for your answer!
$endgroup$
– Studentu
Jan 13 at 18:09
add a comment |
$begingroup$
Fix $x,y$ and take $p$ such that $x, y in p$. Now take the formula $Phi = ( z = x lor z = y)$ and apply the axiom of specification on $p$.
answered Jan 12 at 17:40
Lucas HenriqueLucas Henrique
1,032414
$endgroup$
$begingroup$
Thank you for answering!
$endgroup$
– Studentu
Jan 13 at 18:09
add a comment |
$begingroup$
Fix $x,y$ and take $p$ such that $x, y in p$. Now take the formula $Phi = ( z = x lor z = y)$ and apply the axiom of specification on $p$.
answered Jan 12 at 17:40
Lucas HenriqueLucas Henrique
1,032414
$endgroup$
$begingroup$
Thank you for answering!
$endgroup$
– Studentu
Jan 13 at 18:09
add a comment |
$begingroup$
Fix $x,y$ and take $p$ such that $x, y in p$. Now take the formula $Phi = ( z = x lor z = y)$ and apply the axiom of specification on $p$.
answered Jan 12 at 17:40
Lucas HenriqueLucas Henrique
1,032414
$endgroup$
Fix $x,y$ and take $p$ such that $x, y in p$. Now take the formula $Phi = ( z = x lor z = y)$ and apply the axiom of specification on $p$.
answered Jan 12 at 17:40
Lucas HenriqueLucas Henrique
1,032414
edited Jan 12 at 20:46
answered Jan 12 at 17:40
Lucas HenriqueLucas Henrique
1,032414
answered Jan 12 at 17:40
Lucas HenriqueLucas Henrique
1,032414
answered Jan 12 at 17:40
Lucas HenriqueLucas Henrique
1,032414
1,032414
$begingroup$
Thank you for answering!
$endgroup$
– Studentu
Jan 13 at 18:09
add a comment |
$begingroup$
Thank you for answering!
$endgroup$
– Studentu
Jan 13 at 18:09
$begingroup$
Thank you for answering!
$endgroup$
– Studentu
Jan 13 at 18:09
$begingroup$
Thank you for answering!
$endgroup$
– Studentu
Jan 13 at 18:09
add a comment |
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