 Key examples of properties of instant-based models of time that cannot be expressed by first-order sentences, but require a second-order language with quantification over sets, are continuity, well-ordering, and the finite interval property. Continuity demands that there be no gaps in the temporal order. Not only must the temporal order be dense, it must also be Dedekind complete, i.e., every non-empty set of time instants that has an upper bound has a least upper bound. An example is the ordered set of real numbers, while a non-example is the ordering of the rational numbers: consider e.g. the set of all rational numbers whose square is less than 2. An instant-based model of time is well-ordered if every non-empty, linear set of time instants has a least element, and it has the finite interval property if between any two subsequent time instants there are at most finitely many instants. The natural numbers are well-ordered and have the finite interval property, the negative integers are not well-ordered but still have the finite interval property, and the positive rationals or reals are neither well-ordered nor do they have the finite interval property. As we will see in  Section 3.6,  these second-order properties can be expressed in propositional temporal languages.