CXL (Compute Express Link) is an emerging open industry-standard interconnect between processing and memory devices that is expected to revolutionize the way systems are designed. It enables cache-coherent, shared memory pools in a disaggregated fashion at unprecedented scales, allowing algorithms to interact with various storage devices using simple loads and stores. While CXL unleashes unique opportunities, it also introduces challenges of data management and crash consistency. For example, CXL currently lacks an adequate programming model, making it impossible to reason about the correctness and behavior of systems on top. In this work, we present CXL0, the first programming model for concurrent programs over CXL. We propose a high-level abstraction for memory accesses and formally define operational semantics. We demonstrate that CXL0 captures a wide range of current and future CXL setups and perform initial measurements on real hardware. To illustrate the usefulness of CXL0, we present a general transformation that enhances any linearizable concurrent algorithm with durability in a distributed partial-crash setting. We believe that this work will serve as a stepping stone for systems design and programming on top of CXL.