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Totally indescribable cardinal
A
cardinal number
κ is called
totally indescribable
iff
for every
proposition
φ and every A ⊆ V
κ
with (V
κ
, ∈, A) ⊧ φ there exists an α < κ with (V
α
, ∈, A ∩ V
α
) ⊧ φ.
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