features. We write $\detfa_{N} = \{\blockfa_{1},\ldots,\blockfa_{K}\}$, where $K$ is the number of features. An example feature allocation of $[6]$ is $\detfa_{6} = \{\{2,3\},\{2,4,6\},\{3\},\{3\},\{3\}\}$. Similarly, a feature allocation $\detfa_{\infty}$ of $\mathbb{N}$ is a multiset of non-empty subsets of $\mathbb{N}$ such that no index $n$ belongs to infinitely many features. The total number of features in this case may be infinite, in which case we write $\detfa_{\infty} = \{\blockfa_{1},\blockfa_{2},\ldots\}$. An example feature allocation of $\mathbb{N}$ is $\detfa_{\infty} = \{\{n: n \textrm{ is prime}\}, \{n: n \textrm{ is not divisible by two}\}\}$. Finally, we may have $K=0$, and $\detfa_{\infty} = \emptyset$ is a valid feature allocation.

A *partition* is a special case of a feature allocation for which the features are restricted to be mutually exclusive and exhaustive. The features of a partition are often referred to as *blocks* or *clusters*. We note that a partition is always a feature allocation, but the converse statement does not hold in general; neither of the examples given above ($\detfa_{6}$ and $\detfa_{\infty}$) are partitions.

We now turn to the problem of defining exchangeable feature allocations, extending previous work on exchangeable random partitions [@aldous:1985:exchangeability]. Let $\randfasp_{N}$ be the space of all feature allocations of $[N]$. A *random 