Abstract
The formal system S1 is considered in the language of set theory with an extremely strong reflection principle. It is proved that the principle is incompatible with the Gödel-Bernays theory. In S1, however, we drop the assumption that each set is a class, and replace it by a weaker statement through which the consistency of S1 seems somewhat credible. In this system, all theorems ZF, as well as some statements on the existence of large cardinals, are provable. It is also shown that if S1 is consistent then it is compatible with the constructibility axiom.
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References
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Additional information
Translated fromAlgebra i Logika, Vol. 37, No. 2, pp. 127–143, March–April, 1998.
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Ganov, V.A. The frames of application of the reflection principle. Algebr Logic 37, 69–77 (1998). https://doi.org/10.1007/BF02671593
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DOI: https://doi.org/10.1007/BF02671593