Linked from

The 13 pages that link to Second-order logic, each with the reason it gives.

• First-order logicCompared with: It expresses some structural claims unavailable to first-order quantification over objects alone.

• Model theoryCompared with: Its greater expressive power comes with different completeness and compactness behavior.

• Predicate logicBroader topic: It expands first-order predicate logic by quantifying over properties and relations.

• Compactness theoremCompared with: Under standard semantics, second-order logic does not have the first-order compactness property.

• Universal quantificationCompared with: Quantifying over properties can express claims that first-order universal quantification cannot capture categorically.

• LogicismRelated: Frege’s arithmetic depends on second-order principles stronger than ordinary first-order logic.

• Peano axiomsRelated: Its induction axiom quantifies over every property, giving the natural numbers a categorical characterization.

• Axiom schemaCompared with: Some principles expressed by schemas in first-order logic can be stated with second-order quantifiers.

• Higher-order logicBroader topic: It is the most familiar level in the hierarchy of higher-order logics.

• Tarski's axiomsCompared with: Second-order axioms can express geometric continuity more categorically than first-order formulations.

• Skolem's paradoxCompared with: Full second-order semantics changes the range of quantification, but does not make the first-order result contradictory.

• Frege's theoremNarrower topic: The theorem's strength comes from quantifying over concepts, not individuals alone.

• Lindström's theoremCompared with: Its greater expressive power comes at the cost of first-order compactness under standard semantics.