Chains of strongly non-reflexive dual groups of integer-valued continuous functions |
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Authors: | Haruto Ohta |
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Institution: | Faculty of Education, Shizuoka University, Ohya, Shizuoka, 422 Japan |
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Abstract: | Answering a question of Eklof-Mekler (Almost free modules, set-theoretic methods, North-Holland, Amsterdam, 1990), we prove: (1) If there exists a non-reflecting stationary set of consisting of ordinals of cofinality for each , then there exist abelian groups such that and for each . (2) There exist abelian groups such that for each and for each . The groups are the groups of -valued continuous functions on a topological space and their dual groups. |
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Keywords: | Abelian group continuous function dual group reflexivity strong non-reflexivity $\mathbb{Z}$-compact |
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