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The 3-stratifiable theorems of \(\text{NFU}_\infty\). (English) Zbl 0972.03051
Summary: It is shown that the 3-stratifiable sentences are equivalent in NFU to truth-functional combinations of sentences about objects, sets of objects, sets of sets of objects, and sentences stating that there are at least \(n\) urelements. This is then used to characterize the closed 3-stratifiable theorems of NFU with an externally infinite number of urelements, as those that can be nearly proved in TTU with an externally infinite number of urelements. As a byproduct we obtain a rather simple demonstration of the consistency of 3-stratifiable extensions of NFU.
MSC:
03E70 Nonclassical and second-order set theories
03B15 Higher-order logic; type theory (MSC2010)
03B30 Foundations of classical theories (including reverse mathematics)
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