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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.
2
votes
Expressive power of FO with $\mu$
You also might be interested in the paper The Role of Decidability in First Order Separations over Classes of Finite
Structures by Steven Lindell and Scott Weinstein. While they don't address the abov …
6
votes
1
answer
202
views
Finite-variable fragments of $\Delta_0$-formulas
Consider sets definable in the usual structure of arithmetic $(\mathbb{N},0,1,+,\times)$ by $\Delta_0$-formulas, i.e., formulas with bounded quantifiers. The quantifier alternation hierarchy has been …