The Bounded Proper Forcing Axiom

@article{Goldstern1995TheBP,
  title={The Bounded Proper Forcing Axiom},
  author={Martin Goldstern and Saharon Shelah},
  journal={J. Symb. Log.},
  year={1995},
  volume={60},
  pages={58-73}
}
The bounded proper forcing axiom BPFA is the statement that for any family of @1 many maximal antichains of a proper forcing notion, each of size @1, there is a directed set meeting all these antichains. A regular cardinalis called §1-re∞ecting, if for any regular cardinal ´, for all formulas ', \H(´) j= '''" implies \9-<•, H(-)j= '''" We show that BPFA is equivalent to the statement that two nonisomorphic models of size @1 cannot be made isomorphic by a proper forcing notion, and we show that… 

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