Modules and Infinitary Logics
Saharon Shelah · Contemporary mathematics - American Mathematical Society · 2012
We deal with abelian groups and R R -modules. We consider theories in infinitary logic of the form L λ , θ \mathbb {L}_{\lambda ,\theta } of such structures M M and prove they have elimination of quantifiers up to positive existential formulas, so ones defining subgroups of some power of M M . Hence in the appropriate sense those theories are stable and understood to some extent.