This is, what, 7 years old? Never mind. Read it anyway. Has problems, but what doesn't?. As for the comments. I suppose this is what we get these days, young minds, keen to show what they know, whilst not wanting to contemplate what they don't. Shame really. If universes are likely to display are large number of 'real' constructs represented by a large variety of mathematical objects then, yes, Ramsey-type arguments will come into play. Two things: Ramsey Theory is distinct from Ramsey's Theorem. If you want a 'rule of thumb' then,well, there it is. It is kinda like the helpful anti-demon of what you find in other areas of complexity. Rather than telling you, if you put a particular idea into a certain format that better men have failed, it tells you to look harder, there is something. But it is just about mathematical objects and will always work if your problem fits. It will give huge bounds. But, crucially, these bounds are just the worse possible case: if what you are looking at is purely random. Which is unlikely. There will be rules, otherwise your problem is, well, just a Ramsey Theorem re-statement. So, two things, the 'real' bounds will be lower, likely sharply, if you can find the 'reason'. And, of course, there will be a reason which might lead to all sorts of other interesting things. (Look at the Happy Ending Problem for an example). 'Ramsey-Type' can mean any 'type' of such result. Symmetry Breaking comes from Erdos's work on using his probabilistic method, Turan, loads of stuff.

This is, what, 7 years old? Never mind. Read it anyway. Has problems, but what doesn't?. As for the comments. I suppose this is what we get these days, young minds, keen to show what they know, whilst not wanting to contemplate what they don't. Shame really. If universes are likely to display are large number of 'real' constructs represented by a large variety of mathematical objects then, yes, Ramsey-type arguments will come into play. Two things: Ramsey Theory is distinct from Ramsey's Theorem. If you want a 'rule of thumb' then,well, there it is. It is kinda like the helpful anti-demon of what you find in other areas of complexity. Rather than telling you, if you put a particular idea into a certain format that better men have failed, it tells you to look harder, there is something. But it is just about mathematical objects and will always work if your problem fits. It will give huge bounds. But, crucially, these bounds are just the worse possible case: if what you are looking at is purely random. Which is unlikely. There will be rules, otherwise your problem is, well, just a Ramsey Theorem re-statement. So, two things, the 'real' bounds will be lower, likely sharply, if you can find the 'reason'. And, of course, there will be a reason which might lead to all sorts of other interesting things. (Look at the Happy Ending Problem for an example). 'Ramsey-Type' can mean any 'type' of such result. Symmetry Breaking comes from Erdos's work on using his probabilistic method, Turan, loads of stuff.