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Stream: learning: questions

Topic: Changing cofinality of a regular uncountable cardinal

Jan Pax (Feb 07 2024 at 17:39):

Is it possible to change the cofinality of a regular uncountable cardinal without collapsing any cardinal, and at best, is it possible to do so without any semi-axiom beyond ZFC ?

James Hanson (Feb 15 2024 at 21:25):

What do you mean by 'semi-axiom'? Is this a technical term or are you just referring to assumptions beyond ZFC in general?

Prikry forcing is one of the standard tools for changing cofinalities without collapsing cardinals, but it uses a measurable cardinal. My vague impression is that this is something that's hard to arrange in general.

David Michael Roberts (Feb 16 2024 at 00:35):

This would make a good MathOverflow question, there are set theorists there who know this stuff well.

Jan Pax (Feb 17 2024 at 19:10):

by semi-axiom I mean existence of a measurable cardinal, CH and similar. My MathOverflow question has been closed because of the shorthenes of my question without appreciating how good (IMHO) it is.

Todd Trimble (Feb 17 2024 at 23:25):

Jan Pax said:

by semi-axiom I mean existence of a measurable cardinal, CH and similar. My MathOverflow question has been closed because of the shorthenes of my question without appreciating how good (IMHO) it is.

Could you give the title of the question? If the question is good, then it should be reopened.

Jan Pax (Feb 18 2024 at 09:07):

The question is now even hidden, click on this link

David Michael Roberts (Feb 18 2024 at 10:03):

You should ask it on MathOverflow. Two MathOverflow mods are participating in this discussion, and it seems both are interested in seeing the question...

David Michael Roberts (Feb 18 2024 at 10:04):

The link you give is to Math.stackexchange, where we have no powers to see such questions.

Jan Pax (Feb 18 2024 at 10:19):

Please see here

David Michael Roberts (Feb 18 2024 at 10:58):

What was your original motivation? Including that helps a short question go down better

Jan Pax (Feb 18 2024 at 15:29):

My motivation stems from the fact, that there might be a wrong opinion that if you collapse a cofinality which is by definition a regular cardinal, then you would collapse this regular cardinal as well.

John Baez (Feb 18 2024 at 18:15):

I'm glad the question is back on MathoverFlow, together with an answer.

David Michael Roberts (Feb 18 2024 at 22:02):

That answer is unexpected to me! But I'm not an expert, in any case

Morgan Rogers (he/him) (Feb 19 2024 at 09:22):

The word "equiconsistent" is wonderful, I'm going to keep that one in my back pocket.