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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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Is non-connectedness of graphs first order axiomatizable?

I haven't thought about model theory in a while but I'll give this a shot. First, by bi-infinte graph, I assume that you mean $\mathbb{Z}$ in which the only edges are those adjoining adjacent vertices …
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