Gödel's God

A friend referred me to a Wikipedia page where Kurt Godel has claimed to have proven that God exists. http://en.wikipedia.org/wiki/Gödel’s_ontological_proof
The proof says
1. Existence is a positive property in all worlds.
2. God of a world is defined as the sum total of all positive properties in a world.
3. At least something exists in every world.
4. So a God exists in every world.
Here are my objections:
a. Point 1 cannot be accepted. Existence is defined as a positive property. A negative property exits. So what is it? Positive or negative?
b. Point 2 cannot be accepted. Why restrict God to only positive properties? If God is limited, then how can he be God? Defining God as a limited entity is not acceptable.
c. Why bring in “world” here? Why not apply the logic to the collection of everything that exists? Then the same argument will lead to one God for the entire universe, which is better.
The Advaita Vedanta uses a similar logic:
1. God is defined as Existence (sat) and Consciousness (chit)
2. At least something exists and is conscious. To deny this, the denier has to exist and be conscious. So it cannot be denied.
3. So God exists.
Once you have defined God as Existence itself, then the question “Does God exist?” is equivalent to “Does Existence exit?”, which has to be obviously true. Advaita Vedanta does the same thing and Godel also seems to do the same thing. Advaita Vedanta’s premises and conclusion are more generic and cleaner than Godel’s.