The embodiments set forth techniques for generating snapshots of file system volumes without requiring the implementation of reference counts. A file system can manage snapshot identifiers (IDs) within an object map that corresponds to the file system volume, where each snapshot ID represents a different existing snapshot of the file system volume. A new snapshot can be generated simply by (1) establishing a new snapshot ID based on a current transaction ID managed for the file system volume, and (2) closing the current transaction ID and generating a new current transaction ID. In turn, the new current transaction ID is assigned as a transaction ID within mapping entries that are established/updated after the snapshot is established. In this manner, the transaction ID assigned to each mapping entry can be analyzed against the snapshot IDs to determine the snapshots (if any) to which the mapping entry corresponds.