Is the arduino uno compatible with 4D arrays?

[system]

You mean like this:

// save some unsigned ints
PROGMEM  prog_uint16_t charSet[]  = { 65000, 32796, 16843, 10, 11234};
...
...
// read back a 2-byte int
 displayInt = pgm_read_word_near(charSet + k)

?