Research seminar, Kurt Gödel Research Center – October 9th
Abstract: Least fixed points of monotone operators are well-studied objects in many
areas of mathematical logic. Typically, they are characterized as the
intersection of all sets closed under the respective operator or as the
result of its iteration from below.
In this talk I will start off from specific $\Sigma_1$ operators in a
Kripke-Platek environment and relate fixed point assertions to alternative
set existence principles. By doing that, we are also led to some
“largeness axioms” and to several open problems.