Using the Bounded Comprehension Principle, show that if x and y are sets then

so are:

a.

b.

c.

I'm just not sure the Bounded Comprehension Principle applies here... could someone explain this?

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- Jan 19th 2011, 02:14 PMgutnedawgBounded Comprehension Principle
Using the Bounded Comprehension Principle, show that if x and y are sets then

so are:

a.

b.

c.

I'm just not sure the Bounded Comprehension Principle applies here... could someone explain this? - Jan 19th 2011, 03:58 PMDrSteve
Let me try the first one:

(to answer the question you only need the first equation) - Jan 19th 2011, 04:43 PMgutnedawg
I guess I wasn't clear in my description

You have to demonstrate that for all of the sets - Jan 19th 2011, 04:54 PMgutnedawg
- Jan 19th 2011, 07:20 PMDrSteve
P(x) is the Power Set of x, that is .

Since x is a set, so is P(x) (by the power set axiom).

I realize that you need to do all of them. I did the first one to start you off. If you understand this one, then you should at least be able to attempt the other two. Give them a try, show your thoughts, and I'll help out if you get stuck. - Jan 19th 2011, 07:25 PMgutnedawg
I don't understand how this is using the bounded comprehension principle

- Jan 19th 2011, 07:35 PMDrSteve
The Comprehension schema

Bounded Comprehension is where is a set. - Jan 19th 2011, 08:09 PMgutnedawg
- Jan 19th 2011, 08:39 PMDrSteve
I've never heard that definition, but it is equivalent to the one I have given you. For example, if has rank , the rank of can be expressed in terms of (I think it has rank ). Conversely you can find a bounding set for a collection of sets of rank less than a fixed ordinal.