# Asaf Karagila - Countable unions of countable sets and the power of their power sets without the Axiom of Choice

Dates: | 9 October 2019 |
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Times: | 15:00 - 15:00 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

Who is it for: | University staff, External researchers, Current University students |

Speaker: | Asaf Karagila |

Asaf Karagila joins us for the Logic Seminar.

How large is a countable union of countable sets? Assuming ZFC, the answer is simple: it's countable, and in particular its power set has the same size as the real numbers. Assuming only ZF it turns out that we cannot say a whole lot about countable unions of countable sets, and we can say even less about their power sets. We will present some theorems regarding what we can and cannot determine about countable unions of countable sets and about their power sets, and see that ZF is even weaker than ZFC when it comes to saying something concrete about power sets of infinite sets.

### Speaker

Asaf Karagila

Organisation: UEA