/bin/sh is hardly ever a Bourne shell on any systems nowadays (even Solaris which was one of the last major vendors to include it have now switched to a POSIX sh for their /bin/sh in Solaris 11).
/bin/sh was the Thomson shell in the early 70s. The Bourne shell replaced it in Unix V7 in 1979.
/bin/sh has been the Bourne shell for many years thereafter (or the Almquist shell, a free reimplementation on BSDs).
/bin/sh is more commonly an interpreter or another for the POSIX
sh language which is itself a subset of the language of ksh88 (and a superset of the Bourne shell language with some incompatibilities).
The Bourne or POSIX sh don't have arrays. Or rather they have only one array: the positional parameters (
$@, so one array per function as well).
ksh88 did have arrays which you set with
set -A, but that didn't get specified in the POSIX sh as the syntax is awkward and not very usable.
Other shells with array/lists variables include:
bash (which mostly copied the ksh syntax the ksh93 way),
fish each with a different syntax (
rc the shell of the once to-be sucessor of Unix,
zsh being the most consistent ones)...
sh (also works in modern versions of the Bourne shell):
set '1st element' 2 3 # setting the array
set -- "$@" more # adding elements to the array
shift 2 # popping elements from the array
printf '<%s>\n' "$@" # passing all the elements of the $@ array
# as arguments to a command
for i do # looping over the elements of the $@ array ($1, $2...)
printf 'Looping over "%s"\n' "$i"
printf '%s\n' "$1" # accessing individual element of the array.