proper forcing axiom

Also known as PFA

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