Alphabeta Math
RemarkRemark: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-14
How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

  • Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
  • AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
  • AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Easton-support orientation for many regular cardinals

Remark

The one-cardinal construction in Higher Cohen forcing violates GCH at a regular cardinal does not control a whole continuum function by naive iteration: full support can destroy closure, while finite support at uncountable coordinates can destroy the intended chain condition. Easton forcing instead uses support bounded below every regular cardinal when combining higher Cohen factors.

Any proposed regular-cardinal continuum function F must at least be monotone and satisfy cf⁡(F(κ))>κ; the latter is the König obstruction from König's theorem: assuming the Axiom of Choice, if κi<λi for every i∈I then ∑i∈Iκi<∏i∈Iλi. This is orientation only. It asserts neither Easton's realization theorem nor any singular-cardinal prescription.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

19 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources