Maximal almost disjoint families, determinacy, and forcing
Publikation: Bog/antologi/afhandling/rapport › Ph.d.-afhandling › Forskning
This thesis is based on [5], which is joint work with David Schrittesserand Asger Tornquist. We study the notion of J -MAD families where Jis a Borel ideal on !. We show that if J is an arbitrary F ideal,or is any nite or countably iterated Fubini product of F ideals, thenthere are no analytic innite J -MAD families; and assuming ProjectiveDeterminacy there are no innite projective J -MAD families; and underthe full Axiom of Determinacy + V LpRq there are no innite J -madfamilies. These results apply in particular when J is the ideal of nitesets Fin, which corresponds to the classical notion of MAD families. Theproofs combine ideas from invariant descriptive set theory and forcing
Originalsprog | Engelsk |
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Status | Udgivet - 2019 |
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ID: 222547700