We study Σ₁(ω₁)-definable sets (i.e., sets that are equal to the collection of all sets satisfying a certain Σ₁-formula with parameter ω₁) in the presence of large cardinals. Our results show that the ...

This is a preview. Log in through your library . Abstract We try to count the number of countable models M of T with a fixed set Q = φ (M) of realizations of a type φ. Also, for stable T, we define an ...