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Results tagged with lo.logic
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user 167587
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.
15
votes
0
answers
237
views
Natural examples of Borel surjections without right inverse
As discussed in this question, in general a Borel surjection $f:\mathbb{R}\rightarrow\mathbb{R}$ may not have a Borel right inverse, namely a $g$ such that $f\circ g=id$, although there is always a co …
- 623
13
votes
1
answer
266
views
Descriptive complexity of analytic continuation
Consider the set of complex power series
$$
f(z)=\sum_{n=0}^\infty a_nz^n
$$ that have radius of convergence $1$ and can be analytically continued to the neighborhood of some point on the unit circle. …
- 623
0
votes
Some "axiom of choice" and "dependent choice" issues
The answer to (2) actually depends on the exact meaning of "strictly larger", since cardinalities without choice are a mess. Working in ZF+DC, if $\mathcal{B}$ is a countably generated $\sigma$-algebr …
- 623