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Mat. Zametki, 2005, Volume 78, Issue 6, Pages 864–869 (Mi mz2658)  

On the Cardinality of the Family of Precomplete Classes in $P_E$

S. S. Marchenkov

M. V. Lomonosov Moscow State University

Abstract: Let $E$ be an infinite set of cardinality $\mathbf m$, and let $P_E$ be the set of all functions defined on $E$. We prove that the cardinality of the family of all classes precomplete in $P_E$ is equal to $2^{2^{\mathbf m}}$. If $C_{\mathbb R}$ is the set of all continuous functions of real variables, then the cardinality of the family of all classes precomplete in $C_{\mathbb R}$ is equal to $2^{2^{\aleph_0}}$.

DOI: https://doi.org/10.4213/mzm2658

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English version:
Mathematical Notes, 2005, 78:6, 801–806

Bibliographic databases:

UDC: 519.716
Received: 18.03.2003

Citation: S. S. Marchenkov, “On the Cardinality of the Family of Precomplete Classes in $P_E$”, Mat. Zametki, 78:6 (2005), 864–869; Math. Notes, 78:6 (2005), 801–806

Citation in format AMSBIB
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