calcification 发表于 2025-3-21 19:05:47
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Second order arithmetic if we temporarily assume as an axiom that a problem P is solvable, how difficult is it to . that a second problem Q is solvable? If we can prove that Q is solvable under the assumption that P is solvable, this gives us information that Q is “weaker” than P, at least modulo the other axioms used inIndecisive 发表于 2025-3-22 10:02:53
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Set theory and beyond”.We cannot easily talk about . (equivalence classes of well orderings) as such in Z., but many properties of the ordinals can be formulated in terms of specific well orderings instead. We have already seen that ATR. can express many such properties quite naturally. In this chapter, we investigate a情感脆弱 发表于 2025-3-22 22:26:51
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Problem reducibilitiesr does not, then we may view the latter as “harder” from a certain computational standpoint. But it is not obvious how to find such a class for a particular pair of problems, or whether such a class even exists. It is also unclear what relationship this kind of classification really expresses.