Elements of Finite Model Theory¶
Libkin, L. (2004). Elements of Finite Model Theory. Springer.
Cited by¶
2 citations across 1 artifact.
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Domain-specific¶
- Quantifier Rank
- Leonid Libkin uses this definition to form the bounded fragment \(\mathrm{FO}[k]\) of first-order formulas whose rank is at most \(k\).
This sourceDefines quantifier rank and \(\mathrm{FO}[k]\), distinguishes it from total quantifier count and prenex count, and connects rank to Ehrenfeucht–Fraïssé equivalence.
- For a fixed finite relational vocabulary and fixed tuple of free variables, Libkin proves that only finitely many \(\mathrm{FO}[k]\) formulas exist up to logical equivalence and that rank-\(k\) types can themselves be represented by formulas of rank \(k\).
This sourceEstablishes finiteness up to equivalence and rank-\(k\) type results for fixed finite relational vocabularies and fixed free-variable arity.
- Leonid Libkin uses this definition to form the bounded fragment \(\mathrm{FO}[k]\) of first-order formulas whose rank is at most \(k\).
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