Distributed Ledgers (e.g. Bitcoin) occupy currently the first lines of the economical and political media and many speculations are done with respect to their level of coherence and their computability power. Interestingly, there is no consensus on the properties and abstractions that fully capture the behaviour of distributed ledgers. The interest in formalising the behaviour of distributed ledgers is twofold. Firstly, it helps to prove the correctness of the algorithms that implement existing distributed ledgers and explore their limits with respect to an unfriendly environment and target applications. % Secondly, it facilitates the identification of the minimal building blocks necessary to implement the distributed ledger in a specific environment. Even though the behaviour of distributed ledgers is similar to abstractions that have been deeply studied for decades in distributed systems no abstraction is sufficiently powerful to capture the distributed ledger behaviour. This paper introduces the Distributed Ledger Register, a register that mimics the behaviour of one of the most popular distributed ledger, i.e. the Bitcoin ledger. The aim of our work is to provide formal guarantees on the coherent evolution of Bitcoin. We furthermore show that the Bitcoin blockchain maintenance algorithm verifies the distributed ledger register properties under strict conditions. Moreover, we prove that the Distributed Ledger Register verifies the regularity register specification. It follows that the strongest coherency implemented by Bitcoin is regularity under strong assumptions (i.e. partial synchronous systems and sparse reads). This study contradicts the common belief that Bitcoin implements strong coherency criteria in a totally asynchronous system. To the best of our knowledge, our work is the first one that makes the connection between the distributed ledgers and the classical theory of distributed shared registers.