I am reading in Jech's Set Theory the chapter about large cardinals. After discussing measurable cardinals he moves on to weakly-compact cardinals, which have been discussed far earlier in the book.
I went back to the chapter dealing with weakly-compact cardinals and began retracing the definition.

Eventually, it came into this:

We denote $[k]^n = \{X \subseteq \kappa\mid |X| = n\}$. If $\lambda$ is a cardinal, we denote $\kappa \to (\lambda)^2$ when for every partition of $[\kappa]^2$ into $2$ we have $H \subseteq \kappa$ that is of cardinality $\lambda$, and for which $[H]^2$ is strictly in one part.

And we say that $\kappa$ is weakly-compact if it satisfies the property $\kappa \to (\kappa)^2$.

The problem is that I'm a bit lost in all those definitions, and not even sure about the $\kappa \to (\lambda)^2$ notation. 

My questions are, if so, can someone help me make some sense into those definitions, and is there an equivalent definition for weakly-compact cardinals which can help me understand their properties better?


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