ABSTRACT

However, this class is not first-order definable, so I don’t know whether one might hope to prove that for any first-order theory T we have either

(ii") there is a A assignment of elements of 2N as complete invariants,

would be extremely interesting, and sufficient to prove Vaught’s conjecture under large cardinal assumptions, or even prove Vaught’s conjecture outright in ZFC if, as is most likely, one could obtain

§8. More reading. There is always more to read. In this case especially there are a number of issues we only touched on which could have been discussed at length.