Maximal Nonfinitely Generated Subalgebras
نویسنده
چکیده
We show that “every countable algebra with a nonfinitely generated subalgebra has a maximal nonfinitely generated subalgebra” is provably equivalent to ’1-CA0 over RCA0.
منابع مشابه
A modular inherently nonfinitely based lattice
Proof. As observed in McNulty [7], a locally finite variety V of finite type is inherently nonfinitely based if and only if for infinitely many natural numbers N , there is a non-locally-finite algebra each of whose N -generated subalgebras belongs to V. We prove the theorem by establishing these facts. We assume the reader is familiar with the basic facts of modular lattices; see [1], [2], [6]...
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