Axiomatic Set Theory — Continuum Hypothesis & Independence

graph TD ZFC["ZFC\n(Charts 1–3)"] DefCH["Def: CH\n2^ℵ₀ = ℵ₁"] DefGCH["Def: GCH\n∀α ℵα₊₁ = 2^ℵα"] DefL["Def: Constructible L\nL = ⋃ Lα"] T1["Thm: L ⊨ ZFC\nGödel"] T2["Thm: L ⊨ CH\nGödel 1940"] T3["Thm: Con(ZFC) → Con(ZFC+CH)\nCH not disprovable"] T4["Thm: Con(ZFC) → Con(ZFC+¬CH)\nCohen 1963"] T5["Thm: CH independent of ZFC\nGödel + Cohen"] DefForcing["Def: Forcing\nM, P, G, M[G]"] ZFC --> DefCH ZFC --> DefGCH ZFC --> DefL DefL --> T1 T1 --> T2 T2 --> T3 ZFC --> DefForcing DefForcing --> T4 T3 --> T5 T4 --> T5 classDef axiom fill:#ff6b6b,color:#fff,stroke:#c0392b classDef definition fill:#b197fc,color:#fff,stroke:#9775fa classDef theorem fill:#51cf66,color:#fff,stroke:#40c057 class ZFC axiom class DefCH,DefGCH,DefL,DefForcing definition class T1,T2,T3,T4,T5 theorem