1-In the first week of October, he said that they would meet in the next week.
2-In the first week of October, he said that they would meet over the next week.
3-In the first week of October, he said that they would meet the next week.
4-In the first week of October, he said that they would meet next week.

In which case:
a-we are talking about the next calendar week
and in which case:
b-we are talking about the next seven days

Does 2 imply that they were supposed to meet more then once?
Can the others be used in this case?

Does 4 not imply that they are supposed to meet in the week following the week in which 4 is uttered? For instance, if 4 is uttered in the third week of January 2014, would it not imply that they are supposed to meet in the fourth week of January 2014?

Gratefully,
Navi.

Gratefully,
Navi.