Rothmaler, Philipp Some model theory of modules. III: On infiniteness of sets definable in modules. (English) Zbl 0524.03020 J. Symb. Log. 49, 32-46 (1984). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 1 Document MSC: 03C35 Categoricity and completeness of theories 16D40 Free, projective, and flat modules and ideals in associative algebras 03C80 Logic with extra quantifiers and operators 16E50 von Neumann regular rings and generalizations (associative algebraic aspects) 03C10 Quantifier elimination, model completeness, and related topics 03C60 Model-theoretic algebra Keywords:modules over an associative ring; positive primitive subgroups; coherence; von Neumann regularity; model completeness; eliminability of cardinality quantifiers; Vaughtian pairs; rings with a unique maximal ideal; infinite module; regular rings; infinite simple ring; completeness; coherent rings; flat modules; definable subsets; there are infinitely many; Ramsey quantifiers; finite cover property Citations:Zbl 0512.03017; Zbl 0471.03022 PDFBibTeX XMLCite \textit{P. Rothmaler}, J. Symb. Log. 49, 32--46 (1984; Zbl 0524.03020) Full Text: DOI References: [1] On strongly minimal sets 36 pp 79– (1971) [2] Magidor-Malitz quantifiers in modules 49 pp 1– (1984) · Zbl 0584.03023 [3] Bulletin de l’Académie Polonaise des Sciences. Série des Sciences Mathématiques, Astronomiques et Physiques 24 pp 543– (1976) [4] DOI: 10.1080/00927877708822167 · Zbl 0352.16011 · doi:10.1080/00927877708822167 [5] Definability problems for modules and rings 36 pp 623– (1971) [6] Decidability and generalized quantifiers (1980) · Zbl 0442.03011 [7] Fundamenta Mathematicae 70 pp 253– (1971) · Zbl 0245.01016 [8] Nagoya Mathematical Journal 27 pp 688– (1966) [9] Lectures on rings and modules (1966) [10] Algebra II (1976) [11] DOI: 10.1016/0003-4843(71)90016-7 · Zbl 0227.02029 · doi:10.1016/0003-4843(71)90016-7 [12] Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences. Séries A et B 272 pp A1289– (1971) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.