axiom schema sentence in Hindi
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- Replacing Axiom Five by an axiom schema one obtains a ( weaker ) first-order theory called " Peano Arithmetic ."
- In the presence of the axiom schema of separation, Russell's paradox becomes a proof that there is no set of all sets.
- With the axiom schema of specification instead of unrestricted comprehension, the conclusion doesn't hold and, hence is not a logical consequence.
- A different objection put forth by Henri Poincar?is that defining sets using the axiom schemas of circularity, into the definitions of mathematical objects.
- An appealing but somewhat mysterious feature of NBG is that its axiom schema of Class Comprehension is equivalent to the conjunction of a finite number of its instances.
- If the new axiom schema is not a tautology, then every formula becomes a theorem ( which makes the concept of a theorem useless in this case ).
- Now, axioms are particular formul?( or, for axiom schemas, rules for constructing formul?) while inference rules describe how to transform formul?into other formul?
- Restrictions such as these are useful as a technique to reduce the number of inference rules or axiom schemas in deductive systems, which leads to shorter proofs of metalogical results.
- If no element E of A satisfies \ theta ( E ) then the set B desired by the relevant instance of the axiom schema of separation is the empty set.
- The axiom schema of specification states that this subset always exists ( it is an axiom " schema " because there is one axiom for each \ phi ).
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