| He showed that was computable, but since only countably many real numbers are computable, most real numbers are not computable. |
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| We build an uncountably categorical but not countably categorical theory whose only computably presentable model is the saturated one. |
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| There are uncountably many subsets of N, but since there are only countably many Turing machines, there can be only countably many decidable sets. |
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| One such is the free Boolean algebra on countably many generators, which is the only countable atomless Boolean algebra. |
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| A subset of X is I-sequentially compact if and only if it is sequentially countably compact in the ordinary sense. |
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| If a set is neither finite nor countably infinite, it is said to be uncountably infinite or simply uncountable. |
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