KnowraSecond-order logicLinked fromLinked fromThe 13 pages that link to Second-order logic, each with the reason it gives.All 13Broader topic 2Related 2Narrower topic 1Compared with 8First-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.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.Axiom schemaCompared with: Some principles expressed by schemas in first-order logic can be stated with second-order quantifiers.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.Lindström's theoremCompared with: Its greater expressive power comes at the cost of first-order compactness under standard semantics.