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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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Are all infinite graphs $3$-weak-edge colorable?
If $E$ is countable, then we can define the function $c$ by induction as follows.
Choose an identification $E = \{1,2,\ldots\}$ and choose $c(1) \in \{1,2,3\}$ arbitrarily. Assume that $c(k)$ is defi …