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Results tagged with lo.logic
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user 48485
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.
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Accepted
Darboux property of non-atomic sigma-additive nonnegative measures equivalent to the AC?
Here is a proof that only uses countable choice. It is taken from Fremlin, Measure Theory, Volume 5, Number 566F. The chapter 56 of this multi-volume work is a great source on the discussion of choice …
- 273
4
votes
Unnecessary uses of the axiom of choice
The supremum of an arbitrary set of measurable functions from a $\sigma$-finite measure space into $\mathbb R\cup \{\pm\infty\}$ exists in the following sense:
Let $F$ be a set of such measurable func …