Mathematical Logic Quarterly

Relations between cardinalities of the finite sequences and the finite subsets of a set

Journal Article


We write seq ( m ) and fin ( m ) for the cardinalities of the set of finite sequences and the set of finite subsets, respectively, of a set which is of cardinality m . With the axiom of choice ( AC ), seq ( m ) = fin ( m ) for every infinite cardinal m but, without AC , any relationship between seq ( m ) and fin ( m ) for an arbitrary infinite cardinal m cannot be proved. In this paper, we give conditions that make seq ( m ) and fin ( m ) comparable for an infinite cardinal m . Among our results, we show that, if we assume the axiom of choice for sets of finite sets, then seq ( m ) = fin ( m ) for every Dedekind‐infinite cardinal m and the condition that m is Dedekind‐infinite cannot be weakened to weakly Dedekind‐infinite.

Related Topics

Related Publications

Related Content

Site Footer


This website is provided by John Wiley & Sons Limited, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ (Company No: 00641132, VAT No: 376766987)

Published features on are checked for statistical accuracy by a panel from the European Network for Business and Industrial Statistics (ENBIS)   to whom Wiley and express their gratitude. This panel are: Ron Kenett, David Steinberg, Shirley Coleman, Irena Ograjenšek, Fabrizio Ruggeri, Rainer Göb, Philippe Castagliola, Xavier Tort-Martorell, Bart De Ketelaere, Antonio Pievatolo, Martina Vandebroek, Lance Mitchell, Gilbert Saporta, Helmut Waldl and Stelios Psarakis.