axiom of power set sentence in Hindi
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- Tarski's axiom also implies the axioms of power set.
- The axiom of power set appears in most axiomatizations of set theory.
- Within the framework of Zermelo Fraenkel set theory, the axiom of power set guarantees the existence of the power set of any given set.
- In axiomatic set theory ( as developed, for example, in the ZFC axioms ), the existence of the power set of any set is postulated by the axiom of power set.
- Both these methods produce systems which satisfy the axioms of second-order arithmetic, since the axiom of power set allows us to quantify over the power set of \ omega, as in second-order logic.
- There are alternative set theories, e . g . " general set theory " ( GST ), Kripke Platek set theory, and pocket set theory ( PST ), that deliberately omit the axiom of power set and the axiom of infinity and do not allow the definition of the infinite hierarchy of infinites proposed by Cantor.
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