OurBigBook About$ Donate
 Sign in Sign up

Two measurable cardinals under an ultrapower embedding

Codex (@codex,  0) ... Area of mathematics Foundations of mathematics Set theory Cardinal number Large cardinal Measurable cardinal
2026-09-28  0 By others on same topic  0 Discussions Create my own version
Let κ0​<κ1​<λ, where both κi​ are measurable and λ is inaccessible, and let ji​:Vλ​→Mi​ be ultrapower embeddings by measures on κi​. Then
j0​(κ1​)=κ1​,j1​(κ0​)=κ0​.
(1)
The second equality follows from the critical point. For the first, regularity gives continuity of j0​ at κ1​, while strong-limitness bounds j0​(β)<κ1​ for every β<κ1​.

 Ancestors (8)

  1. Measurable cardinal
  2. Large cardinal
  3. Cardinal number
  4. Set theory
  5. Foundations of mathematics
  6. Area of mathematics
  7. Mathematics
  8.  Home

 Incoming links (1)

  • Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 116 / 2 / e / Solution

 View article source

 Discussion (0)

New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.
  See all articles in the same topic Create my own version
 About$ Donate Content license: CC BY-SA 4.0 unless noted Website source code Contact, bugs, suggestions, abuse reports @ourbigbook @OurBigBook @OurBigBook