What is meant by the abbreviation 'MSV solution', used in the context of DSGE modeling? What is meant by the abbreviation MSV solution, used in the context of adaptive learning in DSGE modeling? E.g. see Bullard and Mitra (2002)

minimum state variable (MSV) solutions it is in full, but what does that mean?
Minimum state variable (MSV) solution is a special technique used to find an unique equilibrium with desirable properties in DSGE models. Often DSGE models can have multiple paths that will satisfy the conditions given by the system you are modelling. 

Hence to provide some meaningful results you have to somehow choose between the all possible paths/solutions possible. There are multiple ways how to do that. MSV solution is a solution that helps to avoid sunspot equilibria and bubbles (see McCallum (1999)). In addition huge advantage of this approach as pointed out by McCallum is that  "the MSV criterion is designed to yield a single bubble-free solution by construction." It can be also shown that this kind of method is quite efficient and guaranteed to yield unique solution for wide ranges of models (albeit not all). 

As you can see in Bullard and Mitra (2002), they talk about MSV solution when they want to show that there is unique solution that can determine their model coefficients $a,b,c$, so when they talk about MVS solution they are just saying that they applied this approach to select an unique solution this way as opposed to some other one.