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Soundness in this sense (sigma_1 soundness) is defined by equivalency to the standard model (specifically, all sentences provable in the system must be provable
by dogecoinbase 5y ago
Soundness in this sense (sigma_1 soundness) is defined by equivalency to the standard model (specifically, all sentences provable in the system must be provable in the standard model).
- dwohnitmok 5y agoIt is defined by equivalency to a standard model. Whether there is a single standard model is a philosophical question (which granted most, but not all, set theorists tend to agree with). Hence sigma_1 soundness is from a purely mathematical point of view a relative statement.