One of the goals of 5G is to simplify the 4G core network and enable interworking across multiple Radio Access Technologies (RATs) without the addition of specialized network elements, protocols and interfaces that perform often redundant functions for each access technology. Achieving this reduces operator costs, and can improve the subscriber experience when devices can access multiple RATs. In this paper we propose the notion of Access Independent Core Network (AICN) where devices can connect to the core through any technology and consume a set of services. We show that it is possible to achieve access independence through a core network architecture that includes access independent functions, access independent bearer plane protocols, and access independent signaling between the network controller and the device and access switch. We outline benefits of the proposed architecture through examples involving WiFi integration.