Dimitrić, Radoslav M. Trees, inverse systems, and valuated vector spaces. (English) Zbl 1115.18300 Acta Math. Univ. Ostrav. 12, No. 1, 19-22 (2004). Summary: We introduce (perhaps unexpected) correspondence between trees, inverse systems of sets or algebras and valuated vector spaces. We also define \(\kappa\)-inverse systems, Aronszajn and Kurepa inverse systems and use the correspondence to prove new results related to non-triviality of inverse limits of surjective inverse systems. MSC: 18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.) 03E04 Ordered sets and their cofinalities; pcf theory 03E65 Other set-theoretic hypotheses and axioms 03E75 Applications of set theory 16B50 Category-theoretic methods and results in associative algebras (except as in 16D90) × Cite Format Result Cite Review PDF Full Text: EuDML References: [1] Doyle Cutler, Radoslav Dimitrić: Valuated vector spaces, Kurepa’s hypothesis and Abelian p-groups. Rocky Mountain J. Math., 23 (1993), No. 4, 1253-1266. · Zbl 0814.20034 · doi:10.1216/rmjm/1181072491 [2] Radoslav Dimitrić: A note on surjective inverse systems. International J. Pure Appl. Math., 10 (2004), No.3, 349-356. · Zbl 1054.18002 [3] Kenneth Kunen: Set Theory. North-Holland, 1980. · Zbl 0443.03021 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.