topological stable rank one and AF-algebra construction on Cantor set

clique principle – Are Foreman’s maximality precept disproved? Answer

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clique principle – Are Foreman’s maximality precept disproved?

Models and forcing with sizable cardinals already constructed it’s disprove Foreman’s maximality precept?
$PFA$ equiconsistent of supercompact cardinals.
Forsing plane used for Berkeley cardinals.
FMP is sentence about undoubted clique universe love Woodin dichotomy or unostentatious live some mannequin $M$ the place for any universal extention $M(G)$ FMP maintain?

Update: $PFA$ equiconsistent some sizable cardinals.

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