Maths - Sets - NBG

NBG is a rigorous axomatic foundation for set theory based on work by: John von Neuman, Paul Bernays and Kurt Gödel. It is one of many intended to eliminate potential paradoxes, in set theory, pointed out by Bertrand Russel (also see ZF).

The NBG axiomatic formulation makes a distinction between 'sets' and 'classes'. All entities in NBG are classes, the word 'set' is reserved for collections that are members of other classes. nbg

So the outermost 'class' is not a 'set', this is known as a 'proper class'.

The Comprehension Principle is modified by requiring the objects referred to are sets.


If A and B are classes and C and D are sets:

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