Depends on what you mean by "true core".
Intel's HyperThreading just adds an extra set of registers to each core, so if a thread stalls for any reason (branch misprediction, I/O wait, cache miss, or whatever), instead of sitting idle, the execution resource can quickly shift to the instructions in the other set of registers. The two threads scheduled on the one core never run at the same time. So HyperThreading does not increase maximum possible performance at all. It just reduces the time that processor cores spend idle for one reason or another.
AMD's Bulldozer and Piledriver modules are not like a core with HyperThreading. Instead of just an extra set of registers, the module has an extra set of integer execution resources as well. So rather than one thread running when another is stalled, both threads scheduled on the module run at the same time. There are still some other shared resources, like the instruction decoder, but it really is like two separate cores. But only for integer instructions. Each module has only one floating point execution unit, so with floating point code, one module is one core.
The A10-x800K chips use Piledriver modules, so a quad-core chip is a dual-core for floating point instructions and quad-core for integer instructions.