Jared Holshouser will be speaking in this week's GLG seminar on Wednesday, Oct. 26 at 3:45pm in GAB 461. All are welcome!

Jonsson Cardinals in ZFC

In 1962, Bjarni Jonsson asked if there is a cardinal so that every algebra (here considered to be a set along with an at most countable list of functions it is closed under) on that cardinal contains a proper subalgebra (defined in the intuitive way) of full size. He was motivated by the study of universal algebras. It turns out that such a cardinal, henceforth referred to as Jonsson, is a large cardinal of strength below measurable, but still strong enough to deny that V=L. Although this question was initially motivated by algebra, these cardinals are part of the study of cardinal arithmetic, as the existence of a Jonsson cardinal is equivalent to a number of useful set theoretic construction principles. We will be exploring these connections in this talk.