Return to Answer

Cantor's Attic, which I founded with Victoria Gitman, is a compendium of information on the consistency strength hierarchy in set theory, spanning the range from ZFC (which in this context is viewed as a weak theory) up through the large cardinal hierarchy to the strongest notions. Any expert set-theorist is encouraged and welcome to make additions to the database (just create an account and then begin editing). We aim at a comprehensive listing of all the main concepts of infinity, organized in large part by their large cardinal consistency strength.

There are numerous parts of the large cardinal consistency-strength hierarchy that are mapped out in fine detail in various sources. See, for example, the chart in Kanamori's book:

Or Victoria Gitman's chart of the large cardinal hierarchy in the vicinity of Ramsey cardinals, on which she wrote her dissertation:

Or Norman Perlmutter's similar chart for a different region of the large cardinal hierarchy on which he had focussed in his dissertation:

So indeed there are many such charts for the relative consistency strength of the various large cardinal hypotheses studied in set theory. Where to look depends a lot on which particular part of the hierarchy you are interested.

If anyone else knows of good charts of regions of the large cardinal hiearchy available online, I'd appreciate it if you could provide a link. Feel free to post as an answer! (Or it to this answer as an image or at least in the comments.)

Cantor's Attic, which I founded with Victoria Gitman, is a compendium of information on the consistency strength hierarchy in set theory, spanning the range from ZFC (which in this context is viewed as a weak theory) up through the large cardinal hierarchy to the strongest notions. Any expert set-theorist is encouraged and welcome to make additions to the database (just create an account and then begin editing). We aim at a comprehensive listing of all the main concepts of infinity, organized in large part by their large cardinal consistency strength.

There are numerous parts of the large cardinal consistency-strength hierarchy that are mapped out in fine detail in various sources. See, for example, the chart in Kanamori's book:

[![][1]][1]

Or Victoria Gitman's chart of the large cardinal hierarchy in the vicinity of Ramsey cardinals, on which she wrote her dissertation:

[![][2]][2]
_(source: boolesrings.org)

Or Norman Perlmutter's similar chart for a different region of the large cardinal hierarchy on which he had focussed in his dissertation:

[![][3]][3]
_(source: boolesrings.org)

So indeed there are many such charts for the relative consistency strength of the various large cardinal hypotheses studied in set theory. Where to look depends a lot on which particular part of the hierarchy you are interested.

If anyone else knows of good charts of regions of the large cardinal hiearchy available online, I'd appreciate it if you could provide a link. Feel free to post as an answer! (Or it to this answer as an image or at least in the comments.) [1]: https://i.sstatic.net/ZgnI4.jpg [2]: https://i.sstatic.net/rXkCC.jpg [3]: https://i.sstatic.net/ByA0c.jpg

Cantor's Attic, which I founded with Victoria Gitman, is a compendium of information on the consistency strength hierarchy in set theory, spanning the range from ZFC (which in this context is viewed as a weak theory) up through the large cardinal hierarchy to the strongest notions. Any expert set-theorist is encouraged and welcome to make additions to the database (just create an account and then begin editing). We aim at a comprehensive listing of all the main concepts of infinity, organized in large part by their large cardinal consistency strength.

There are numerous parts of the large cardinal consistency-strength hierarchy that are mapped out in fine detail in various sources. See, for example, the chart in Kanamori's book:

Or Victoria Gitman's chart of the large cardinal hierarchy in the vicinity of Ramsey cardinals, on which she wrote her dissertation:

http://boolesrings.org/victoriagitman/files/2013/06/ramseydiagram.jpg

Or Norman Perlmutter's similar chart for a different region of the large cardinal hierarchy on which he had focussed in his dissertation:

http://boolesrings.org/perlmutter/files/2013/04/ChartForWebSite.jpg

So indeed there are many such charts for the relative consistency strength of the various large cardinal hypotheses studied in set theory. Where to look depends a lot on which particular part of the hierarchy you are interested.

If anyone else knows of good charts of regions of the large cardinal hiearchy available online, I'd appreciate it if you could provide a link. Feel free to post as an answer! (Or it to this answer as an image or at least in the comments.)

Cantor's Attic, which I founded with Victoria Gitman, is a compendium of information on the consistency strength hierarchy in set theory, spanning the range from ZFC (which in this context is viewed as a weak theory) up through the large cardinal hierarchy to the strongest notions. Any expert set-theorist is encouraged and welcome to make additions to the database (just create an account and then begin editing). We aim at a comprehensive listing of all the main concepts of infinity, organized in large part by their large cardinal consistency strength.

There are numerous parts of the large cardinal consistency-strength hierarchy that are mapped out in fine detail in various sources. See, for example, the chart in Kanamori's book:

Or Victoria Gitman's chart of the large cardinal hierarchy in the vicinity of Ramsey cardinals, on which she wrote her dissertation:

Or Norman Perlmutter's similar chart for a different region of the large cardinal hierarchy on which he had focussed in his dissertation:

So indeed there are many such charts for the relative consistency strength of the various large cardinal hypotheses studied in set theory. Where to look depends a lot on which particular part of the hierarchy you are interested.

If anyone else knows of good charts of regions of the large cardinal hiearchy available online, I'd appreciate it if you could provide a link. Feel free to post as an answer! (Or it to this answer as an image or at least in the comments.)

Cantor's Attic is a compendium of information on the consistency strength hierarchy in set theory, spanning the range from ZFC (which in this context is viewed as a weak theory) up through the large cardinal hierarchy to the strongest notions.

There are numerous parts of the large cardinal consistency-strength hierarchy that are mapped out in fine detail in various sources. See, for example, the chart in Kanamori's book:

Or Victoria Gitman's chart of the large cardinal hierarchy in the vicinity of Ramsey cardinals, on which she wrote her dissertation:

http://boolesrings.org/victoriagitman/files/2013/06/ramseydiagram.jpg

Norman Perlmutter has a similar chart for a different region of the large cardinal hierarchy on which he had focussed in his dissertation:

http://boolesrings.org/perlmutter/files/2013/04/ChartForWebSite.jpg

So indeed there are many such charts for the relative consistency strength of the various large cardinal hypotheses studied in set theory. Where to look depends a lot on which particular part of the hierarchy you are interested.

If anyone else knows of good charts of regions of the large cardinal hiearchy available online, I'd appreciate it if you could provide a link. Feel free to post as an answer! (Or it to this answer as an image or at least in the comments.)

Cantor's Attic, which I founded with Victoria Gitman, is a compendium of information on the consistency strength hierarchy in set theory, spanning the range from ZFC (which in this context is viewed as a weak theory) up through the large cardinal hierarchy to the strongest notions. Any expert set-theorist is encouraged and welcome to make additions to the database (just create an account and then begin editing). We aim at a comprehensive listing of all the main concepts of infinity, organized in large part by their large cardinal consistency strength.

There are numerous parts of the large cardinal consistency-strength hierarchy that are mapped out in fine detail in various sources. See, for example, the chart in Kanamori's book:

Or Victoria Gitman's chart of the large cardinal hierarchy in the vicinity of Ramsey cardinals, on which she wrote her dissertation:

http://boolesrings.org/victoriagitman/files/2013/06/ramseydiagram.jpg

Or Norman Perlmutter's similar chart for a different region of the large cardinal hierarchy on which he had focussed in his dissertation:

http://boolesrings.org/perlmutter/files/2013/04/ChartForWebSite.jpg

So indeed there are many such charts for the relative consistency strength of the various large cardinal hypotheses studied in set theory. Where to look depends a lot on which particular part of the hierarchy you are interested.

If anyone else knows of good charts of regions of the large cardinal hiearchy available online, I'd appreciate it if you could provide a link. Feel free to post as an answer! (Or it to this answer as an image or at least in the comments.)