  Linear temporal logic (LTL) is used in system verification to write formal
specifications for reactive systems. However, some relevant properties, e.g.
non-inference in information flow security, cannot be expressed in LTL. A class
of such properties that has recently received ample attention is known as
hyperproperties. There are two major streams in the research regarding
capturing hyperproperties, namely hyperlogics, which extend LTL with trace
quantifiers (HyperLTL), and logics that employ team semantics, extending truth
to sets of traces. In this article we explore the relation between asynchronous
LTL under set-based team semantics (TeamLTL) and HyperLTL. In particular we
consider the extensions of TeamLTL with the Boolean disjunction and a fragment
of the extension of TeamLTL with the Boolean negation, where the negation
cannot occur in the left-hand side of the Until-operator or within the
Global-operator. We show that TeamLTL extended with the Boolean disjunction is
equi-expressive with the positive Boolean closure of HyperLTL restricted to one
universal quantifier, while the left-downward closed fragment of TeamLTL
extended with the Boolean negation is expressively equivalent with the Boolean
closure of HyperLTL restricted to one universal quantifier.
