The PS4 won't have dedicated servers (except for testing), but apparently SE is anticipating enough new players to be adding some additional servers. Here's an excerpt from a Game Watch interview (as translated by Reinheart):

Quote Originally Posted by Reinheart View Post
GW: PS4 versions beta test is starting finally on 2/22, are you going to open new servers?

Y: At phase 1 stage, we are going to open up several worlds set specifically for the beta test in Japan.

GW: So these are just test servers, and not actual servers for release?

Y: Yes, these are test servers for the PS4. From phase 2 we will start placing new worlds for the NA/EU DC and Japan DC.
*DC - Data Center

GW: Are you going to move over those several test servers into the real servers?

Y: No, we’re going to wipe the data there so that will be different, but we will probably keep the world names and the test server names.

GW: So that’s going to be the new servers aimed for the PS4 version?

Y: We’ll have to see how successful the beta goes, but we are planning to add at least 2 new worlds for each individual DC. For the PC version we are also going to start sale on Steam soon, so I believe we’ll see more player increase.