Arcmage can give up his specialist spell slot?

[isildur]

An archmage gains the opportunity to select a special ability from among those described below by permanently eliminating one existing spell slot (she cannot eliminate a spell slot of higher level than the highest-level spell she can cast). Each special ability has a minimum required spell slot level, as specified in its description.

or can't?

[JoshuaZ]

An archmage gains the opportunity to select a special ability from among those described below by permanently eliminating one existing spell slot (she cannot eliminate a spell slot of higher level than the highest-level spell she can cast). Each special ability has a minimum required spell slot level, as specified in its description.

or can't?

RAW yes they can give it up. This is (I think) part of the assumption going into the summary of the archmage as +0 in the PrC Tier system (http://brilliantgameologists.com/boards/index.php?topic=5198.0). If you don't do this, then the archmage arcana for the most part of substantially less nice for wizards. Note that this doesn't matter for sorcerers entering and since they generally have slightly more spell slots, giving up slots is more ok, although qualifying for archmage is trickier for a sorcerer.

One other cheesy thing to do is to give up spell slots that one gets from some class feature from another PrC before you become an archmahe. Thus for example, one can by RAW give up the spell slots you get from Alienist, or Nightmare Spinner. In the case of Nightmare Spinner, this actually works really nicely given that you had to lose a caster level to enter. But it does border on the sort of thing where you may get a book thrown at you for it.