1 5 Ju l 1 99 8 On inverse γ - systems and the number of L ∞ λ - equivalent , non - isomorphic models for λ singular
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چکیده
Suppose λ is a singular cardinal of uncountable cofinality κ. For a model M of cardinality λ, let No(M) denote the number of isomorphism types of models N of cardinality λ which are L∞λ-equivalent to M. In [She85] Shelah considered inverse κ-systems A of abelian groups and their certain kind of quotient limits Gr(A)/Fact(A). In particular Shelah proved in [She85, Fact 3.10] that for every cardinal μ there exists an inverse κ-system A such that A consists of abelian groups having cardinality at most μ and card (
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For a cardinal κ and a model M of cardinality κ let No(M) denote the number of non-isomorphic models of cardinality κ which are L∞κ-equivalent to M. In [She82] Shelah established that when κ is a weakly compact cardinal and μ ≤ κ is a nonzero cardinal, there exists a model M of cardinality κ with No(M) = μ. We prove here that if κ is a weakly compact cardinal, the question of the possible value...
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