Assume G is a superstable locally modular group. We describe for any countable model M of Th(G) the quotient group G(M) / Gm(M). Here Gm is the modular part of G. Also, under some additional assumptions we describe G(M) / Gm(M) relative to G⁻(M). We prove Vaught's Conjecture for Th(G) relative to Gm and a finite set provided that ℳ(G) = 1 and the ring of pseudoendomorphisms of G is finite.
@article{1172787549,
author = {Newelski, Ludomir},
title = {Relative Vaught's Conjecture for Some Meager Groups},
journal = {Notre Dame J. Formal Logic},
volume = {48},
number = {1},
year = {2007},
pages = { 115-132},
language = {en},
url = {http://dml.mathdoc.fr/item/1172787549}
}
Newelski, Ludomir. Relative Vaught's Conjecture for Some Meager Groups. Notre Dame J. Formal Logic, Tome 48 (2007) no. 1, pp. 115-132. http://gdmltest.u-ga.fr/item/1172787549/