signature=00190e25c7649a78fb3997950abcc58a,Counting Ω-ideals

摘要：

Let \\({\\mathbb{A}}\\) be a universal algebra of signature Ω, and let \\({\\mathcal{I}}\\) be an ideal in the Boolean algebra \\({\\mathcal{P}_{\\mathbb{A}}}\\) of all subsets of \\({\\mathbb{A}}\\) . We say that \\({\\mathcal{I}}\\) is an Ω-ideal if \\({\\mathcal{I}}\\) contains all finite subsets of \\({\\mathbb{A}}\\) and \\({f(A^{n}) \\in \\mathcal{I}}\\) for every n -ary operation \\({f \\in \\Omega}\\) and every \\({A \\in \\mathcal{I}}\\) . We prove that there are \\({2^{2^{\\aleph_0}}}\\) Ω-ideals in \\({\\mathcal{P}_{\\mathbb{A}}}\\) provided that \\({\\mathbb{A}}\\) is countably infinite and Ω is countable.

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