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Article 2594 of comp.ai.philosophy:
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>From: solan@math.uio.no (Svein Olav Nyberg)
Newsgroups: sci.philosophy.tech,sci.logic,comp.ai.philosophy,sci.math
Subject: Aleph-1 - What?
Message-ID: <1992Jan9.141029.13881@ulrik.uio.no>
Date: 9 Jan 92 14:10:29 GMT
References: <1992Jan2.131048.18412@news.stolaf.edu> <1992Jan6.092440.25451@etl.go.jp> <1992Jan6.130008.16471@news.stolaf.edu> <1992Jan7.214019.6969@neptune.inf.ethz.ch> <1992Jan8.170943.15772@aio.jsc.nasa.gov>
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I just wondered: Given the continuum hypothesis, Aleph-1 = 2^Aleph-0 (=c).
Given its converse, that there exists (at least) a cardinal number between
Aleph-0  and  2^Aleph-0, does it make sense to speak of Aleph-1, the
least cardinal larger than Aleph-0? 
With the denial of the continuum hypothesis, what is to stop us from
saying that given any two cardinal numbers n,m, n<m, there might be some third
cardinal number p such that n<p<m?

Solan


