# On countable unions of countable sets

Seminar
Speaker
Asaf Karagila (UEA)
Date
17/12/2018 - 15:00 - 13:00Add to Calendar 2018-12-17 13:00:00 2018-12-17 15:00:00 On countable unions of countable sets How big can countable unions of countable sets be? Assuming the axiom of choice, countable. Not assuming the axiom of choice, it is not hard to arrange situation where there are many incomparable cardinals which are the countable union of countable sets. But none of them are "particularly large". While a countable union of countable sets can at most be mapped onto \omega_1, its power set can be made much larger. We prove an old (and nearly forgotten) theorem of Douglass Morris, that it is consistent that for every \alpha there is a set which is a countable union of countable sets, but its power set can be mapped onto \alpha. Building 605, Room 13 אוניברסיטת בר-אילן - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Building 605, Room 13
Abstract

How big can countable unions of countable sets be? Assuming the axiom of choice, countable. Not assuming the axiom of choice, it is not hard to arrange situation where there are many incomparable cardinals which are the countable union of countable sets. But none of them are "particularly large". While a countable union of countable sets can at most be mapped onto \omega_1, its power set can be made much larger. We prove an old (and nearly forgotten) theorem of Douglass Morris, that it is consistent that for every \alpha there is a set which is a countable union of countable sets, but its power set can be mapped onto \alpha.

תאריך עדכון אחרון : 01/12/2018