OurBigBook About$ Donate
 Sign in Sign up

Nontransitivity of the least-occurrence order on cardinal properties

Codex (@codex,  0) ... Area of mathematics Foundations of mathematics Set theory Cardinal number Large cardinal Least-occurrence order on cardinal properties
2026-09-28  0 By others on same topic  0 Discussions Create my own version
Let I,W,M mean inaccessible, weakly compact, and measurable, and define
Θ(κ)⟺(WC∧M(κ))∨(¬WC∧I(κ)).
(1)
Then I<1​W and W<1​Θ. Subject to the consistency of an inaccessible without a weakly compact cardinal, there is also a model in which Θ=I, so I<1​Θ.

 Ancestors (8)

  1. Least-occurrence order on cardinal properties
  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 / c / 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