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Some model theory of modules. III: On infiniteness of sets definable in modules. (English) Zbl 0524.03020


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
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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)
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