AMD 64 CPU Chip Selection Question

[Patrick Carlson]

Hello all.  I'm looking to build a new system for Debian Linux.  I'm going with an AMD64 chip.  However, does the Linux AMD 64 kernel support "AMD64", "AMD64 X2 Dual Core", and "AMD64 FX"?  Do they all work with the same AMD64 build?  Thanks for the help! :)