Descending Distributive Forcing

Calliope Ryan-Smith (--)

Sep 10. 2026, 11:30 — 12:00

Distributivity is a fundamental property of notions of forcing that describes the (non)-creation of new sequences of ground model elements. The utility and importance of this cannot be overstated, with an archetypal application being the forcing of the Continuum Hypothesis without adding new real numbers. Descending distributivity is a weakening of this property, more closely related to the (non)-creation of fresh sequences. Much as freshness is a notion of 'new functions added locally at an ordinal', descending distributivity is tied closely to locally new behaviour in the forcing extension. We will introduce descending distributive forcing, some of its properties, and its applications to fresh functions (in an AC context) and the axiom of extendable choice (in a non-AC context).

Further Information
Venue:
ESI Boltzmann Lecture Hall
Associated Event:
FLINTA* in Set Theory (Workshop)
Organizer(s):
Hope Duncan (U Leeds)
Azul Fatalini (U Leeds)
Martina Iannella (TU Wien)
Siiri Kivimäki (U Helsinki)
Sandra Müller (TU Wien)
Lena Wallner (TU Wien)