  In this work, I investigate several combinatorial properties of Borel (or
co-analytic) ideals on countable sets. I extend a theorem presented in M.
Hru\v{s}\'{a}k, D. Meza-Alc\'antara, E. Th\"ummel, and C. Uzc\'ategui,
\emph{Ramsey Type Properties of Ideals}, and also find an $F_\sigma$ tall ideal
in which player II has a winning strategy in the Cut and Choose Game, which was
a question posed by J. Zapletal. In the second section, I present some Ramsey
properties of ideals, such as the previously known fact that the random graph
ideal is critical for the Ramsey property (for subsets of size two and
colorings with two colors) and construct a critical ideal for every Ramsey
property. The third section includes comments on the Solecki ideal, and in the
fourth section, I discover an $F_\sigma$ tall $K$-uniform ideal that is not
equivalent to $\mathcal{ ED }_{fin}$, which is a question from Michael
Hru\v{s}\'ak's.
