492 reputation
411
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location Montreal, Canada
age 41
visits member for 4 years, 1 month
seen May 10 at 23:33

I have no properties.


Aug
6
comment Has anyone ever proposed additional axioms?
Adding axioms makes more theorems provable. They need not be though of as truths. You can add either the Axiom of Choice or its denial to standard set theory, extending the set of theorems in disjoint ways. On one natural interpretation of that, only one of those two sets of novel theorems is a set of truths.
Aug
6
comment Has anyone ever proposed additional axioms?
Cohen showed that neither Choice nor the Continuum Hypothesis could be proved in ZF. It was earlier work of Goedel's that showed that they cannot be disproved in ZF.
Jul
28
comment Higher Order Logics
Yes. This is why I said "A further sense in which Higher Order Logics with standard or saturated semantics (HOL, hereafter)".