Hoffelner, S. (2025). The global Σn+21-uniformization property and BPFA. Advances in Mathematics, 470, Article 110272. https://doi.org/10.1016/j.aim.2025.110272
Set Theory; Descriptive Set Theory; Projective sets; Forcing Axioms
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Abstract:
We show that given a reflecting cardinal, one can produce a model of BPFA where the Σ<inf>n</inf><sup>1</sup>-uniformization property holds simultaneously for all n≥2 which stands in stark constrast to the situation under PFA. We do this via a new forcing construction which gets rid of the delimitations caused by a good projective well-order of the reals, which has been the sole tool to obtain global Σ-uniformization since 1959.
