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NuMachine, as powerful as Turing machine, but more intuitive in its working is described. Adding three more derivation rules to Elementary Arithmetic of Godel and calling it Sentient Arithmetic (SA), the incompleteness theorems are proved within SA, without using any metalanguage. Intuitive Set Theory (IST), a theory in which we do not have to deal with cardinals higher than aleph-null, is described. In IST, there is no Skolem Paradox and there are no nonLebesgue measurable sets.
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