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Where Is the Simplest Proof of Main Claim 1.3 on Page 46 of Shelah's “Cardinal Arithmetic�
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Where is the simplest proof of Main Claim 1.3 on page 46 of Shelah's book "Cardinal Arithmetic"? It apparently is also Theorem VI.5.8 of Eklof and Mekler's book, "Almost Free Modules:Set-theoretic Methods," but it is not proven there.
For the statement, see
Where can I find a proof of Shelah mentioned in the book "Almost Free Modules" as Theorem VI.5.8?
set-theory cardinals
asked 4 hours ago
Tri
1596
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up vote
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Where is the simplest proof of Main Claim 1.3 on page 46 of Shelah's book "Cardinal Arithmetic"? It apparently is also Theorem VI.5.8 of Eklof and Mekler's book, "Almost Free Modules:Set-theoretic Methods," but it is not proven there.
For the statement, see
Where can I find a proof of Shelah mentioned in the book "Almost Free Modules" as Theorem VI.5.8?
set-theory cardinals
asked 4 hours ago
Tri
1596
We can't know what "simplest" means from your perspective.
– amWhy
3 hours ago
There might be a survey article that gives a complete proof but doesn't require having to wade through the material Shelah's proof depends upon. To be honest, "any other proof" might suit me.
– Tri
3 hours ago
It has been some time that read it and I did not look very carefully before citing the references below but I have delayed enough answering it. If something does not look correct, please just ask.
– Gabriel Fernandes
42 mins ago
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Where is the simplest proof of Main Claim 1.3 on page 46 of Shelah's book "Cardinal Arithmetic"? It apparently is also Theorem VI.5.8 of Eklof and Mekler's book, "Almost Free Modules:Set-theoretic Methods," but it is not proven there.
For the statement, see
Where can I find a proof of Shelah mentioned in the book "Almost Free Modules" as Theorem VI.5.8?
set-theory cardinals
asked 4 hours ago
Tri
1596
Where is the simplest proof of Main Claim 1.3 on page 46 of Shelah's book "Cardinal Arithmetic"? It apparently is also Theorem VI.5.8 of Eklof and Mekler's book, "Almost Free Modules:Set-theoretic Methods," but it is not proven there.
For the statement, see
Where can I find a proof of Shelah mentioned in the book "Almost Free Modules" as Theorem VI.5.8?
set-theory cardinals
asked 4 hours ago
Tri
1596
asked 4 hours ago
Tri
1596
asked 4 hours ago
Tri
1596
asked 4 hours ago
Tri
1596
1596
We can't know what "simplest" means from your perspective.
– amWhy
3 hours ago
There might be a survey article that gives a complete proof but doesn't require having to wade through the material Shelah's proof depends upon. To be honest, "any other proof" might suit me.
– Tri
3 hours ago
It has been some time that read it and I did not look very carefully before citing the references below but I have delayed enough answering it. If something does not look correct, please just ask.
– Gabriel Fernandes
42 mins ago
add a comment |Â
We can't know what "simplest" means from your perspective.
– amWhy
3 hours ago
There might be a survey article that gives a complete proof but doesn't require having to wade through the material Shelah's proof depends upon. To be honest, "any other proof" might suit me.
– Tri
3 hours ago
It has been some time that read it and I did not look very carefully before citing the references below but I have delayed enough answering it. If something does not look correct, please just ask.
– Gabriel Fernandes
42 mins ago
We can't know what "simplest" means from your perspective.
– amWhy
3 hours ago
We can't know what "simplest" means from your perspective.
– amWhy
3 hours ago
There might be a survey article that gives a complete proof but doesn't require having to wade through the material Shelah's proof depends upon. To be honest, "any other proof" might suit me.
– Tri
3 hours ago
There might be a survey article that gives a complete proof but doesn't require having to wade through the material Shelah's proof depends upon. To be honest, "any other proof" might suit me.
– Tri
3 hours ago
It has been some time that read it and I did not look very carefully before citing the references below but I have delayed enough answering it. If something does not look correct, please just ask.
– Gabriel Fernandes
42 mins ago
It has been some time that read it and I did not look very carefully before citing the references below but I have delayed enough answering it. If something does not look correct, please just ask.
– Gabriel Fernandes
42 mins ago
add a comment |Â
1 Answer
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You might want to take a look in [Shelah's pcf theory and its applications] (link below) by Burke and Magidor section 2.
There is another version of the 1.3 in Introduction to Cardinal Arithmetic by Holz, Michael, Steffens, Karsten, Weitz, E.; it is section 3.2 there.
I can not point now where exactly is 1.3 in the handbook chapter by Uri Abraham and Menachem Magidor, but I strongly recommend taking a look there .
If later you look for a proof of trichotomy theorem, (I did not read it but I believe it is simpler than ''Cardinal Arithmetic'') see the appendix in Exact upper bounds and their uses in set theory by Menachem Kojman (rmk: the handbook chapter develops enough so that trichotomy theorem is exercise 2.27)
1 https://www.sciencedirect.com/science/article/pii/0168007290900579
answered 42 mins ago
Gabriel Fernandes
36128
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
You might want to take a look in [Shelah's pcf theory and its applications] (link below) by Burke and Magidor section 2.
There is another version of the 1.3 in Introduction to Cardinal Arithmetic by Holz, Michael, Steffens, Karsten, Weitz, E.; it is section 3.2 there.
I can not point now where exactly is 1.3 in the handbook chapter by Uri Abraham and Menachem Magidor, but I strongly recommend taking a look there .
If later you look for a proof of trichotomy theorem, (I did not read it but I believe it is simpler than ''Cardinal Arithmetic'') see the appendix in Exact upper bounds and their uses in set theory by Menachem Kojman (rmk: the handbook chapter develops enough so that trichotomy theorem is exercise 2.27)
1 https://www.sciencedirect.com/science/article/pii/0168007290900579
answered 42 mins ago
Gabriel Fernandes
36128
add a comment |Â
up vote
0
down vote
You might want to take a look in [Shelah's pcf theory and its applications] (link below) by Burke and Magidor section 2.
There is another version of the 1.3 in Introduction to Cardinal Arithmetic by Holz, Michael, Steffens, Karsten, Weitz, E.; it is section 3.2 there.
I can not point now where exactly is 1.3 in the handbook chapter by Uri Abraham and Menachem Magidor, but I strongly recommend taking a look there .
If later you look for a proof of trichotomy theorem, (I did not read it but I believe it is simpler than ''Cardinal Arithmetic'') see the appendix in Exact upper bounds and their uses in set theory by Menachem Kojman (rmk: the handbook chapter develops enough so that trichotomy theorem is exercise 2.27)
1 https://www.sciencedirect.com/science/article/pii/0168007290900579
answered 42 mins ago
Gabriel Fernandes
36128
add a comment |Â
up vote
0
down vote
up vote
0
down vote
You might want to take a look in [Shelah's pcf theory and its applications] (link below) by Burke and Magidor section 2.
There is another version of the 1.3 in Introduction to Cardinal Arithmetic by Holz, Michael, Steffens, Karsten, Weitz, E.; it is section 3.2 there.
I can not point now where exactly is 1.3 in the handbook chapter by Uri Abraham and Menachem Magidor, but I strongly recommend taking a look there .
If later you look for a proof of trichotomy theorem, (I did not read it but I believe it is simpler than ''Cardinal Arithmetic'') see the appendix in Exact upper bounds and their uses in set theory by Menachem Kojman (rmk: the handbook chapter develops enough so that trichotomy theorem is exercise 2.27)
1 https://www.sciencedirect.com/science/article/pii/0168007290900579
answered 42 mins ago
Gabriel Fernandes
36128
You might want to take a look in [Shelah's pcf theory and its applications] (link below) by Burke and Magidor section 2.
There is another version of the 1.3 in Introduction to Cardinal Arithmetic by Holz, Michael, Steffens, Karsten, Weitz, E.; it is section 3.2 there.
I can not point now where exactly is 1.3 in the handbook chapter by Uri Abraham and Menachem Magidor, but I strongly recommend taking a look there .
If later you look for a proof of trichotomy theorem, (I did not read it but I believe it is simpler than ''Cardinal Arithmetic'') see the appendix in Exact upper bounds and their uses in set theory by Menachem Kojman (rmk: the handbook chapter develops enough so that trichotomy theorem is exercise 2.27)
1 https://www.sciencedirect.com/science/article/pii/0168007290900579
answered 42 mins ago
Gabriel Fernandes
36128
answered 42 mins ago
Gabriel Fernandes
36128
answered 42 mins ago
Gabriel Fernandes
36128
answered 42 mins ago
Gabriel Fernandes
36128
36128
add a comment |Â
add a comment |Â
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We can't know what "simplest" means from your perspective.
– amWhy
3 hours ago
There might be a survey article that gives a complete proof but doesn't require having to wade through the material Shelah's proof depends upon. To be honest, "any other proof" might suit me.
– Tri
3 hours ago
It has been some time that read it and I did not look very carefully before citing the references below but I have delayed enough answering it. If something does not look correct, please just ask.
– Gabriel Fernandes
42 mins ago