(adsbygoogle = window.adsbygoogle || []).push({}); PLEASE help me understand this paper! (Formal math stuff)

Right now in my class we're being given a short introduction to theoretical CS. We're learning not from a book but from our teacher's Ph.D. thesis! The thesis is HEAVY on formal math and I can't follow it... I've been trying for DAYS and have spent many, many hours reading around but it's not making sense. I'm officially desperate now and so I've come here to ask if I could possibly get some help from you guys.

Here's the part I'm stuck on, it's about Turing machines:

http://img105.imageshack.us/img105/5915/help27ib.th.jpg [Broken]

I've been reading a lot and I now understand the distinction between an Urelement and natural numbers as defined with sets (with the axiom of infinity). It's the rest of the paper that I don't get.If any of you could explain to me what the paper is saying possibly with some examples (especially of the Sq thing) then I would be very greatful.If you're pressed for time then here are the parts I'm most confused about:

- What does the Sq
_{(w)}(A) thing mean!?!? If A is, say, { a, b, c }, then what would Sq_{(w)}(A) be? Can you lay it out for me (i.e. write out the elements of the set in set notation { ... })?- In the definition part, when it says "Let A be a set, u, v in Sq
_{(w)}(A)" what does that really mean? If something is an element of Sq_{(w)}(A) then what does it look like?

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# Homework Help: PLEASE help me understand this paper!

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