# 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

**Wikidata**: [Q749043](https://www.wikidata.org/wiki/Q749043)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Proper_forcing_axiom)  
**Source**: https://4ort.xyz/entity/proper-forcing-axiom