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Results tagged with independence-results
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This tag is for questions about proving that some statement is independent from a theory, meaning it is neither provable nor refutable from that theory. Common examples are the continuum hypothesis from the axioms of ZFC, and the axiom of choice from the axioms of ZF.
6
votes
When can a function defined on $[a, b] \cup [b, c]$ be constructively extended to a function...
I am going to work Bishop-style (in particular I am giving myself countable choice, we can try to get rid of it later).
Observe that the Cauchy completion of $[a,b] \cup [b,c]$ is $[a,c]$. For this to …
- 48.8k
18
votes
What's the earliest result (outside of logic) that cannot be proven constructively?
According to Wikipedia, in 5th century BCE, Bryson of Heraclea spoke of a special case of the intermediate value theorem. If we're very generous, that would be an early occurrence of a constructively …
- 48.8k