Russell's type theory, ZF set theory

  • Thread starter Euclid
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What are the weaknesses and strengths of Russell's type theory? I'm having trouble understanding exactly what makes it weaker than ZF. I've been told its too restrictive, but what exactly makes it more restrictive than ZF?
Are there any objections to ZF?
 
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Russell's type theory has some philosophical embellishments, such as the axiom of reducibility, which asserts that every formula is equivalent to another formula that is predicable. This does two things: it makes the restriction redundant, and it is actually not a very plausible axiom. If you must use a theory of types, don't use Russell's, use a simplified theory without the silly redundancies.
 

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