A Distributed Ledger Object (DLO) is a concurrent object that maintains a totally ordered sequence of records, and supports two basic operations: append, which appends a record at the end of the sequence, and get, which returns the sequence of records. In this work we provide a proper formalization of a Byzantine-tolerant Distributed Ledger Object (BDLO), which is a DLO in a distributed system in which processes may deviate arbitrarily from their indented behavior, i.e. they may be Byzantine. Our formal definition is accompanied by algorithms to implement BDLOs by utilizing an underlying Byzantine Atomic Broadcast service. We then utilize the BDLO implementations to solve the Atomic Appends problem against Byzantine processes. The Atomic Appends problem emerges when several clients have records to append, the record of each client has to be appended to a different BDLO, and it must be guaranteed that either all records are appended or none. We present distributed algorithms implementing solutions for the Atomic Appends problem when the clients (which are involved in the appends) and the servers (which maintain the BDLOs) may be Byzantine.