OpenFrontiers
Join
← Back to the index
OP-8658Status unassessedLogic and foundations

Uniform Indiscernibles · Question 25

From ℵ2 to infinity · Historical workshop question

MSC 03 · Mathematical logic and foundations

Editorial mapping of AIMPL source category: Logic. http://aimpl.org/alephtwo/ Not an author-supplied MSC code.

Historical list · status unassessedAs of 2026-09-08Source & evidence ↓
Read original source ↗ 0Submit progressLean 4 ↓Discussion (0)

Problem statement

  • Is u2(ω1)=ω3u_2(\omega_1)=\omega_3 consistent with (sufficiently) large cardinals?

  • How to increase u2(ω1)u_2(\omega_1) without collapsing ω1\omega_1 or ω2\omega_2?

Lean 4

Not yet attached

No Lean statement or proof is attached yet. Have a formalization? Share its source to add it to this problem.

Share a formalization →Verification guide ↗

Background

Question context

Let κ\kappa be an infinite cardinal and put λ=κ+\lambda=\kappa^+. Define u2(κ)=sup⁡{(λ+)L[A]:A⊆κ}u_2(\kappa)=\sup\left\{(\lambda^+)^{L[A]}:A\subseteq\kappa\right\}.

Progress & source assessment

Historical workshop record. Current open/solved status has not been independently reassessed.

The source supplies no status note for this question.

References
  1. [1]From ℵ2 to infinity link

Recorded progress

Add yours →

Nothing recorded yet. A pointer to a paper the entry is missing counts.

Machine attempts

0 recorded

Attempts run against the statement below and are recorded in full, including the failures. The point is to stop the next model — and the next person — from re-walking a road that is already known to end. Each attempt costs 25 credits.

No machine attempts recorded.

Sign in to run an attempt. New accounts start with enough credits for ten.

Discussion

0 notes

Notes are for clarifying the statement, flagging a missing reference, or recording why an approach fails. Claimed solutions belong in a submission, where they can be reviewed.

No notes yet.

Sign in to add a note.