2020/10/05 by Sean Cox, Cox, Sean, Philipp Lücke +1
Computer Science · Mathematics · #03E35 #03E47 #03E57 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.2010.01922
openalex publication_date 2020/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the influence of strong forcing axioms on the complexity of the non-stationary ideal on ω2 and its restrictions to certain cofinalities. Our main result shows that the strengthening MM++ of Martin's Maximum does not decide whether the restriction of the non-stationary ideal on ω2 to sets of ordinals of countable cofinality is Δ1-definable by formulas with parameters in H(ω3). The techniques developed in the proof of this result also allow us to prove analogous results for the full non-stationary ideal on ω2 and strong forcing axioms that are compatible with CH. Finally, we answer a question of S. Friedman, Wu and Zdomskyyshow by showing that the Δ1-definability of the non-stationary ideal on ω2 is compatible with arbitrary large values of the continuum function at ω2.