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Results tagged with lo.logic
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user 22989
first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.
46
votes
Accepted
Do vector spaces without choice satisfy Cantor-Schroeder-Bernstein?
Without the axiom of choice, it is possible that there is a vector space $U\neq 0$ over a field $k$ with no nonzero linear functionals.
Let $V$ be the direct sum of countably many copies of $U$, and $ …
- 35.2k
12
votes
5
answers
1k
views
Does k(X) have a k-basis for every set X, without AC?
This question is inspired by Pace Nielsen's recent question Does a left basis imply a right basis, without AC?.
For any field $k$, the field $k(x)$ of rational functions in one variable has an explic …
CommunityBot
- 1
3
votes
Does a left basis imply a right basis, without AC?
This is a very incomplete answer, but maybe others can fill in the gaps (and I'll try to).
[Edit: I've not been able to make this idea work, although the ideas may lead somewhere, so I'll leave this …
- 35.2k