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Second-order logic

In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic is in turn extended by higher-order logic and type theory.

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Overview

Examples

Syntax and fragments

Semantics

Expressive power

Deductive systems

Non-reducibility to first-order logic

Metalogical results

History and disputed value

Relation to computational complexity

Works cited

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Second-order logic

Nodes126
Edges125
Triples154
Avg. degree1.98
Density0.015873
Components1

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Second-order logic

Top relations

related to Further reading · 60
Second-order logic → An EATCS Series, An Introduction, Andrews, Be, Be Some Values, Berlin, Boolos, Completeness, Erich, Finite, First-order, First-Order Logic, George, Grädel, Harvard University Press, Hendricks, Hilary, Historia Mathematica, Human Face, In
related to Works cited · 27
Second-order logic → Archived, Bulletin, Case, Clarendon Press, Completeness, Foundationalism, Foundations, Fundamentals, Henkin, Hinman, ISBN, Journal, JSTOR, Logic, Mathematical Logic, Mathematics, October, Oxford, PDF, Peters
related to history · 18
Second-order logic → After, Alfred North Whitehead, Arithmetic, Bertrand Russell, Eventually, Fraenkel, Frege, Frege's, Gödel, However, It, Peirce, Predicate, Putnam, Russell's, Skolem's, The, Zermelo
related to Expressive power · 15
Second-order logic → Any, Bigl, Bigr, For, Here, If, In, It, Löwenheim, On, Second-order, Skolem, The, Thus, To
related to Semantics · 7
Second-order logic → Henkin, In, It, Only, The, Thus, Unlike
related to Syntax and fragments · 7
Second-order logic → For, If, In, Sets, St, The, These
related to Relation to computational complexity · 5
Second-order logic → Cayley, Conversely, Pa, The, This
related to Deductive systems · 4
Second-order logic → Each, Several, The, This
related to Mathematical induction · 3
Second-order logic → But, In, Peano
related to Definition of equality · 2
Second-order logic → In, Objects

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Important terminology

second-order logic first-order set semantics displaystyle theory variables domain sets formulas theorem henkin real numbers sentence finite sort standard quantification

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Second-order logicis aextension of first-order logic0.90text
second-order arithmeticinstance ofLindström's theorem imports that Henkin models are just disguised first-order models.For theories0.80text
the existence of non-standard interpretations of higher-order domains isn't just a deficiency of the particular axiomatisation derived from type theory that Henkin usedinstance ofLindström's theorem imports that Henkin models are just disguised first-order models.For theories0.80text
but a necessary consequence of Gödel's incompleteness theoreminstance ofLindström's theorem imports that Henkin models are just disguised first-order models.For theories0.80text
Second-order logicrelated to Deductive systemsSeveral0.60section
Second-order logicrelated to Deductive systemsEach0.60section
Second-order logicrelated to Deductive systemsThe0.60section
Second-order logicrelated to Deductive systemsThis0.60section
Second-order logicrelated to Definition of equalityObjects0.60section
Second-order logicrelated to Definition of equalityIn0.60section
Second-order logicrelated to Expressive powerSecond-order0.60section
Second-order logicrelated to Expressive powerFor0.60section

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