proper forcing axiom (Q749043)

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set theory axiom that if 𝑃 is a proper forcing and 𝐷(𝛼) is a dense subset of 𝑃 for each 𝛼<ω₁, then there is a filter 𝐺⊆𝑃 such that 𝐷(𝛼)∩𝐺 is nonempty for all 𝛼<ω₁
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proper forcing axiom
set theory axiom that if 𝑃 is a proper forcing and 𝐷(𝛼) is a dense subset of 𝑃 for each 𝛼<ω₁, then there is a filter 𝐺⊆𝑃 such that 𝐷(𝛼)∩𝐺 is nonempty for all 𝛼<ω₁
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