Filter data structures are widely used in various areas of computer science to answer approximate set-membership queries. In many applications, the data grows dynamically, requiring their filters to expand along with the data. However, existing methods for expanding filters cannot maintain stable performance, memory footprint, and false positive rate (FPR) simultaneously. We address this problem with Aleph Filter, which makes the following contributions. (1) It supports all operations (insertions, queries, deletes, etc.) in constant time, no matter how much the data grows. (2) Given an estimate of how much the data will ultimately grow, Aleph Filter provides a memory vs. FPR trade-offs on par with static filters.