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A comment on How many real numbers exist? New proof moves closer to an answer. Parent comment

Re:How many real numbers exist? New proof moves closer to an... by dogecoinbase on Thursday July 15, 2021 @01:41PM (#27847513)
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).
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Re:How many real numbers exist? New proof moves closer to an... by dwohnitmok on Thursday July 15, 2021 @01:57PM (#27847798)
It 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.
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