Ok guys,
Lets keep the confusion to a minimum here!
People might actually read this and be misinformed.
I suggest you look up validation versus certification.
How many sign-off's have you seen in a JAR logbook?
Iain, no offense, but maybe you should investigate the matters at hand a bit before giving advice on a site like this, I know you mean well and probably are a good colleague to your fellow students, but some of your replies appear to be a product of your own imagination.
Scorpio, if you want to fly (legally) in an Italian registered aircraft you need a validation on your FAA PPL, this gives you the same privileges as on your FAA PPL except the night privileges. In addition you will need a 'local' medical and a radiolicense if you plan to fly in airspace where two-way RDO is required (probably a good idea anyway) you can apply for an FCC license in the US, that will be valid as a radio license in Italy also. As far as logging PIC..... What does your certificate say regarding class and category??? Probably airplane single engine land, so if you fly a single engine land airplane you can log PIC, you may want to look into prices with a flying club in the vicinity of where you will be staying, as flying in Europe as quite a different matter pricewise form what you have seen in the US.
Edited for smelling pistakes