Andrei Morozov: "On F-parameterizable models"

ABSTRACT:

I will be speaking on a general method to answer questions like
"Is a group G an elementary subgroup of the group $Sym(\omega)$"?
"Is a group G an elementary subgroup of the group $Aut<Q,< >$"? and many
other questions like this, not only for groups.
The method I suggest shows, for instance, that the groups of all
computable, arithmetical, hyperarithmetical permutations,
$\Pi_n^1$-permutations, $\Sigma_n^1$-permutations ($n\in\omega$) fail to
be elementary subgroups in $Sym(\omega)$.
I also prove some general results on the structure of elementary submodels.