The Ground Axiom

Abstract

The ground axiom is the assertion that the set-theoretic universe is not obtainable by forcing over any inner model. Although this appears at first to be a second-order assertion, it is actually first-order expressible in the language of set theory. This article is the extended abstract for a talk at the 2005 Workshop in Set Theory at the Mathematisches Forschungsinstitut Oberwolfach.

This article appeared in 2005. 3 pages. Commentary can be made on my blog at http://jdh.hamkins.org/thegroundaxiom/