INCOMPLETENESS THEOREM AND A SYSTEM WITHIN WHICH THE CONSTRUCTION OF A NAME OF A SENTENCE IS POSSIBLE

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The main results of the present reserach are following :1 We constructed a logical system within which we can construct a name of a sentence by a proper extention of the standard logical system. We thus enriched the expressive power of the logical system.2 A remarkable feature if the system is that it contains as a theorem a formula that expresses the principle of comprehension. This fact implies that the notions considered to be peculiar to set theory belong to this enriched system. This suggests the inadequacy of the standard logical system the representative means of natural language.3 In the system thus obtained, we can develop a method by means of which we can distinguish singular sentences from general ones. This method leads us to a solution of [the problem of the unique correspondence between the form and the content of a sentence].