Universe means: model of set theory. Goedel's incompleteness theorems guarantee the existence of non-standard models of set theory (and Peano arithmetic). Hamk

Universe means: model of set theory. Goedel's incompleteness theorems guarantee the existence of non-standard models of set theory (and Peano arithmetic). Hamkins cleverly uses non-standard models to construct a single program that can (simplifying a bit) exhibit arbitrary behaviour, depending in which universe (= model of set theory) you interpret it.