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noun\ˈgō-dəlz-, ˈgər-, ˈgœ-\
Definition of GODEL'S THEOREM
: a theorem in advanced logic: in any logical system as complex as or more complex than the arithmetic of the integers there can always be found either a statement which can be shown to be both true and false or a statement whose truth or falsity cannot be deduced from other statements in the system —called also Godel's incompleteness theorem