A lot of databases now actually have different configurations and depending on the settings you set, it can be either CA, CP, AP, etc but can not achieve all three at the same time. Some databases actually make an effort to support all three but still prioritizes them in a certain way.
For example, MySQL can be CP and CA depending on the configurations. By default, it is CA because it follows a master slave paradigm which data is replicated to the slaves. Partition tolerance is sacrificed in the event that a set of the slaves loses the connection to the master and therefore decides to elect a new master creating two masters with their own set of slaves.
However, MySQL also has another configuration which is a clustered configuration. It prioritizes CP over availability eg. the cluster will shutdown if there are not enough live nodes to serve all the data.
There are probably more configurations for MySQL that makes it satisfy other CAP theorem combinations but overall, I just wanted say that it depends on what your system requires. Sometimes databases are better for one configuration vs another so its best to see what kinds of problems that may also occur in using a certain configuration.
As for implementing the CAP theorem, I would advise taking a further look into different databases and how they implement the priorities for the CAP theorem. There are just too many different ways of implementing them eg. generally, the master slave model is used for CA systems, the hash ring for AP systems, etc.
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