Title: Invariance of Ideal Limit Points,
Abstract: Let $\mathcal{I}$ be an analytic P-ideal [respectively, a summable ideal] on
the positive integers and let $(x_n)$ be a sequence taking values in a metric
space $X$. First, it is shown that the set of ideal limit points of $(x_n)$ is
an $F_\sigma$-set [resp., a closet set]. Let us assume that $X$ is also
separable and the ideal $\mathcal{I}$ satisfies certain additional assumptions,
which however includes several well-known examples, e.g., the collection of
sets with zero asymptotic density, sets with zero logarithmic density, and some
summable ideals. Then, it is shown that the set of ideal limit points of
$(x_n)$ is equal to the set of ideal limit points of almost all its
subsequences.