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feat: singular cardinals#37098

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vihdzp:singular
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feat: singular cardinals#37098
vihdzp wants to merge 27 commits intoleanprover-community:masterfrom
vihdzp:singular

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@vihdzp vihdzp commented Mar 24, 2026 •
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We define a singular cardinal as an infinite cardinal which is larger than its cofinality. That's to say, every cardinal is exactly one of the following three: finite, regular, or singular.

Re-opened from #17005, with permission.

Co-authored-by: Nir Paz [email protected]

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@vihdzp vihdzp mentioned this pull request Mar 24, 2026
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github-actions bot commented Mar 24, 2026 •
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PR summary e5dfb6ba70

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference

Declarations diff

+ IsRegular.not_isSingular
+ IsSingular
+ IsSingular.aleph_omega0_le
+ IsSingular.cof_ord_lt
+ IsSingular.isSuccLimit
+ IsSingular.isSuccLimit_of_aleph
+ IsSingular.natCast_lt
+ IsSingular.not_isRegular
+ IsSingular.pos
+ aleph0_lt_aleph
+ isRegular_or_isSingular
+ isSingular_aleph_iff
+ isSingular_aleph_omega0
+ lt_aleph0_or_isRegular_or_isSingular
+ not_isRegular_aleph_add_one
+ not_isSingular_aleph0
+ not_isSingular_aleph_one
+ not_isSingular_succ

You can run this locally as follows 
## summary with just the declaration names:
./scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh contains some details about this script.

No changes to technical debt.

You can run this locally as

./scripts/reporting/technical-debt-metrics.sh pr_summary
  • The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
  • The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

@github-actions github-actions bot added the t-set-theory Set theory label Mar 24, 2026
@mathlib-dependent-issues mathlib-dependent-issues bot added the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label Mar 24, 2026
This was referenced Mar 24, 2026
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@mathlib-dependent-issues mathlib-dependent-issues bot removed the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label Mar 24, 2026
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mathlib-dependent-issues bot commented Mar 24, 2026

This PR/issue depends on:

plp127
plp127 reviewed Mar 24, 2026
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Comment thread Mathlib/SetTheory/Cardinal/Regular.lean Outdated
@github-actions github-actions bot added the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Mar 24, 2026
@github-actions github-actions bot removed the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Mar 24, 2026
@mathlib-merge-conflicts mathlib-merge-conflicts bot added the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Apr 5, 2026
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mathlib-merge-conflicts bot commented Apr 5, 2026

This pull request has conflicts, please merge master and resolve them.

@github-actions github-actions bot removed the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Apr 5, 2026
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