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 [MO] Is there a tetration for infinite cardinalities? (Question in MO) MphLee Fellow Posts: 95 Threads: 7 Joined: May 2013 12/02/2014, 02:40 PM I'm not really sure that is that easy... The problem is that cardinals and ordinals are different and we need a good recursive definition of the tetration over the cardinals. I mean, is true that $\aleph_0 =\omega$ but we have also that every transfinite ordinal below $\omega_1$ is countable and thus has cardinality $\aleph_0$ $|\omega+1|=\aleph_0$ and I guess that we always have $|\omega\uparrow{}^{\alpha}\omega|=\aleph_0$ For example, all the epsilon ordinals are countable. Back to the topic. Tommy, when you say inaccessible ordinal you mean "strongly inaccesible" cardinals right? The ones that give us models of ZFC? I don't even understand how you can take the natural logarithm of a cardinal number... Note also that cardinal and ordinal exponentiation aren't the same. MathStackExchange account:MphLee « Next Oldest | Next Newest »

 Messages In This Thread [MO] Is there a tetration for infinite cardinalities? (Question in MO) - by Gottfried - 11/30/2014, 10:37 AM RE: [MO] Is there a tetration for infinite cardinalities? (Question in MO) - by MphLee - 11/30/2014, 09:38 PM RE: [MO] Is there a tetration for infinite cardinalities? (Question in MO) - by tommy1729 - 12/01/2014, 11:55 PM RE: [MO] Is there a tetration for infinite cardinalities? (Question in MO) - by sheldonison - 12/02/2014, 02:35 PM RE: [MO] Is there a tetration for infinite cardinalities? (Question in MO) - by MphLee - 12/02/2014, 02:40 PM RE: [MO] Is there a tetration for infinite cardinalities? (Question in MO) - by tommy1729 - 12/04/2014, 12:08 AM RE: [MO] Is there a tetration for infinite cardinalities? (Question in MO) - by MphLee - 12/04/2014, 09:31 AM RE: [MO] Is there a tetration for infinite cardinalities? (Question in MO) - by tommy1729 - 12/04/2014, 01:20 PM RE: [MO] Is there a tetration for infinite cardinalities? (Question in MO) - by MphLee - 12/06/2014, 02:26 PM RE: [MO] Is there a tetration for infinite cardinalities? (Question in MO) - by tommy1729 - 12/07/2014, 05:32 PM RE: [MO] Is there a tetration for infinite cardinalities? (Question in MO) - by MphLee - 12/28/2014, 10:22 PM

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