Geodesic
אn-FREE MODULES OVER COMPLETE DISCRETE VALUATION DOMAINS WITH ALMOST TRIVIAL DUAL*
Glasgow mathematical journal, Tome 55 (2013) no. 2, pp. 369-380

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DOI

A module M over a commutative ring R has an almost trivial dual if there is no homomorphism from M onto a free R-module of countable infinite rank. Using a new combinatorial principle (the אn-Black Box), which is provable in ordinary set theory, we show that for every natural number n, there exist arbitrarily large אn-free R-modules with almost trivial duals, when R is a complete discrete valuation domain. A corresponding result for torsion modules is also obtained.
DOI : 10.1017/S0017089512000614
Mots-clés : 20A15, 20K10, 20K20, 20K21, 20K30, 13B10, 13L05 
GÖBEL, RÜDIGER; SHELAH, SAHARON; STRÜNGMANN, LUTZ. אn-FREE MODULES OVER COMPLETE DISCRETE VALUATION DOMAINS WITH ALMOST TRIVIAL DUAL*. Glasgow mathematical journal, Tome 55 (2013) no. 2, pp. 369-380. doi: 10.1017/S0017089512000614
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     author = {G\"OBEL, R\"UDIGER and SHELAH, SAHARON and STR\"UNGMANN, LUTZ},
     title = {אn-FREE {MODULES} {OVER} {COMPLETE} {DISCRETE} {VALUATION} {DOMAINS} {WITH} {ALMOST} {TRIVIAL} {DUAL*}},
     journal = {Glasgow mathematical journal},
     pages = {369--380},
     year = {2013},
     volume = {55},
     number = {2},
     doi = {10.1017/S0017089512000614},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089512000614/}
}
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