Miha Habič: The generic multiverse, amalgamability, and blockchains

Datum objave: 20. 5. 2019
Seminar za temelje matematike in teoretično računalništvo
Četrtek, 23. 5. 2019, od 11h do 13h, učilnica 3.07, Jadranska 21
Abstract: Given a countable model of set theory, we can look at its generic multiverse: the smallest collection of models containing the given one, and closed under taking forcing extensions and ground models. There is a natural ordering of the multiverse by the subset relation, and the resulting partial order is quite interesting. It has a similar flavour to the Turing degrees, but a significant difference is that there are models in the multiverse that do not have a common upper bound. I will discuss some known results about the generic multiverse as an ordered structure, and (hopefully) present a selection of recent results, joint with Hamkins, Klausner, Verner, and Williams, on the complexities of the multiverse, such as complicated arrangements of nonamalgamable models.

I will start the talk with a brief introduction to forcing, so no particular knowledge of advanced set theory is required for the seminar.