Fall (first) semesters:
The text that I wrote for the 2010/11 version of the course is Foundations of Mathematical Practice.
For the record: Previous editions of my text were called Introductory notes on the foundations of mathematics. The last of these was dated September 14, 2005, and was used in Math 111 that fall:
In fact I started editing that edition after the course (I don't think I got very far):
I also made some notes on exponentiation for possible incorporation: