Broad Infinity and Generation Principles
University of Birmingham
Abstract:
Broad Infinity is a new and arguably intuitive axiom scheme in set
theory. It states that "broad numbers'', which are three-dimensional
trees whose growth is controlled, form a set. If the Axiom of Choice is
assumed, then Broad Infinity is equivalent to the Ord-is-Mahlo scheme:
every closed unbounded class of ordinals contains a regular ordinal.
Whereas the axiom of Infinity leads to generation principles for sets
and families and ordinals, Broad Infinity leads to more advanced
versions of these principles. The talk explains these principles and
how they are related under various prior assumptions: the Axiom of
Choice, the Law of Excluded Middle, and weaker assumptions.