You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.
Jan Pax (Jan 07 2024 at 17:29):Is it possible to change the cofinality of a regular cardinal without collapsing any cardinals ?
David Michael Roberts (Jan 07 2024 at 21:59):A quick search finds Magdor's article Changing cofinality of cardinals, Fundamenta Mathematicae, 99(1):61–71, 1978. though it's changing cofinalities of measurable cardinals (which are regular), which of course extend ZFC.
Jan Pax (Jan 07 2024 at 22:22):do you mean that every cardinal remains the same and just cofinality of a measurable becomes countable ? That would really answer my question.
David Michael Roberts (Jan 08 2024 at 09:56):https://bibliotekanauki.pl/articles/1364212.pdf
A forcing notion is defined by which the cofinality of certain kinds of measurable cardinals can be changed to any given value without collapsing any cardinals.
Chris Grossack (they/them) (Jan 09 2024 at 16:14):I asked a strong set theorist friend of mine (who's actually on the job market right now, just saying :eyes:) and he said this:
Yes, it's consistent that this is the case. If CH holds, then Namba forcing preserves all cardinals while making aleph_2 singular of cofinality omega. If there’s a measurable, then Prikry forcing makes the measurable have cofinality omega while also preserving all cardinals. I’ll get back to you on whether it’s consistent that every cardinal preserving poset is cofinality preserving.