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Exact Consistency Strength of the Proper Forcing Axiom

Determine the exact large-cardinal consistency strength of ZFC plus the Proper Forcing Axiom (PFA): identify its equiconsistency level by matching upper and lower consistency bounds.

Source: Oberwolfach Report 2025/2, Equiconsistencies between strengthenings of PFA and strengthenings of supercompact cardinals.

Status Open Open; the 2025 Oberwolfach report continues to identify the exact consistency strength of PFA as unresolved. Relative consistency from a supercompact cardinal is an upper bound, not an equiconsistency theorem for PFA. Status review date not recorded in this edition

Listed by ProofAtlas. Status qualification is attributed to ProofAtlas; no full resolution is certified here.

References

Primary source

ProofAtlas open problems; Oberwolfach Report 2025/2, Equiconsistencies between strengthenings of PFA and strengthenings of supercompact cardinals

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