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- W1792820147 abstract "We prove that for each universal algebra $(A,mathcal A)$ of cardinality $|A|ge 2$ and an infinite set $X$ of cardinality $|X|ge|mathcal A|$, the $X$-th power $(A^X,mathcal A^X)$ of the algebra $(A,mathcal A)$ contains a free subset $mathcal Fsubset A^X$ of cardinality $|mathcal F|=2^{|X|}$. This generalizes the classical Fichtenholtz-Kantorovitch-Hausdorff result on the existence of an independent family $mathcal Isubsetmathcal P(X)$ of cardinality $|mathcal I|=|mathcal P(X)|$ in the Boolean algebra $mathcal P(X)$ of subsets of an infinite set $X$." @default.
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- W1792820147 date "2012-09-28" @default.
- W1792820147 modified "2023-10-18" @default.
- W1792820147 title "Independent and free sets in universal algebras" @default.
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