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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 this first-order statement true? [closed]
Consider the natural numbers $\mathbb{N}$ as a structure for NBG set theory.
If we interpret the Axiom of Unions in this structure, we get the statement
$(\forall a \in \mathbb{N})$ $(\exists w \in …