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Cardinal characteristics, projective wellorders and large continuum
Fischer, Vera ; Friedman, Sy-David ; Zdomskyy, Lyubomyr, 1983-
We extend the work of Fischer et al. (2011) [Projective wellorders and mad families with large continuum, Ann. Pure Appl. Logic, 162 (2011), pp. 853-862] by presenting a method for controlling ...cardinal characteristics in the presence of a projective wellorder and ▫$2^{\aleph_0} > \aleph_2$▫. This also answers a question of Harrington (1977) [Long projective wellorderings Ann. Math. Logic, 12 (1977), pp. 1-24] by showing that the existence of a ▫$\Delta^1_3$▫ wellorder of the reals is consistent with Martin's axiom and ▫$2^{\aleph_0} > \aleph_3$▫.
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