Abstract
One problem in set theory without the axiom of choice is to find a reasonable way of estimating the size of a non-well-orderable set; in this paper we present evidence which suggests that this may be very hard. Given an arbitrary fixed aleph κ we construct a model of set theory which contains a set X such that if Y ⊆ X then either Y or X - Y is finite, but such that κ can be mapped into S(S(S(X))). So in one sense X is large and in another X is one of the smallest possible infinite sets. (Here S(X) is the power set of X.)
Publisher
Cambridge University Press (CUP)
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Cited by
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1. The structure of amorphous sets;Annals of Pure and Applied Logic;1995-06
2. A question of Babai on groups;Bulletin of the Australian Mathematical Society;1975-12
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