TY - BOOK

T1 - Maximal almost disjoint families, determinacy, and forcing

AU - Haga, Karen Bakke

PY - 2019

Y1 - 2019

N2 - 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

AB - 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

UR - https://soeg.kb.dk/permalink/45KBDK_KGL/1pioq0f/alma99122448538005763

M3 - Ph.D. thesis

BT - Maximal almost disjoint families, determinacy, and forcing

ER -