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Algebraic logic

Definition

In mathematical logic, algebraic logic is the reasoning obtained by manipulating equations with free variables.

Related concepts

A. N. Whitehead Abstract algebraic logic Abstract logic Ackermann set theory Aleph number Alexander Macfarlane Alfred Tarski Algebraic semantics (mathematical logic)Algebraic structure Alphabet (formal languages)American Mathematical Society Annals of Mathematics Argument Arity Atomic formula Atomic model (mathematical logic)Atomic sentence Augustus De Morgan Automata theory Automated theorem proving Axiom Axiom of choice Axiom schema Axiomatic set theory Axiomatic system Axiomatization of Boolean algebras B. G. Teubner Banach–Tarski paradox Bertrand Russell Bijection Binary operation Binary relation Bit Boolean-valued model Boolean algebra Boolean algebra (structure)Boolean algebras canonically defined Boolean function Cambridge University Press Cantor's diagonal argument Cantor's paradox Cantor's theorem Cardinality Cartesian product Categorical theory Category (mathematics)Category of sets Category theory Charles Loewner Charles Sanders Peirce Christine Ladd Church encoding Church–Turing thesis Clarence Irving Lewis Clarence Lewis Class (set theory)Classical logic Codd's theorem Codomain Combinatory logic Compactness theorem Complement (set theory)Complementary relation Complete theory Composition of relations Computability theory Computable function Computable set Computably enumerable set Computer algebra Concrete category Conservative extension Consistency Constructible universe Construction of the real numbers Constructive set theory Continuum hypothesis Converse relation Countable set Cylindric algebra Decidability (logic)Decision problem Deductive system Diagram (mathematical logic)Difunctional Domain of a function Element (mathematics)Elementary diagram Elementary equivalence Elementary function arithmetic Elsevier Empty set Enumeration Equality (mathematics)Equiconsistency Equivalence relation Ernst Schröder (mathematician)Erotetics Euclid's Elements Euclidean geometry Existential quantification Expression (mathematics)Extension by definitions Extension by new constant and function names Extensionality Finitary relation Finite-valued logic Finite model theory Finite set First-order logic Fixed-point logic Forcing (mathematics)Formal concept analysis Formal grammar Formal language Formal proof Formal semantics (logic)Formal system Formation rule Formula Foundations of geometry Foundations of mathematics Free logic Free variables and bound variables Function (mathematics)Functional predicate Fuzzy set General set theory George Boole Giuseppe Peano Google Books Gottfried Wilhelm Leibniz Gottlob Frege Grothendieck universe Ground expression Ground formula Gunther Schmidt Gödel's completeness theorem Gödel's incompleteness theorems Gödel numbering Hajnal Andréka Halting problem Harvard University Press HathiTrust Helena Rasiowa Hereditary set Heterogeneous relation Heyting algebra Higher-order logic Hilbert's axioms Hilbert system History of logic History of mathematical logic Hochschule Karlsruhe Hugh MacColl Image (mathematics)Inaccessible cardinal Inclusion (set theory)Independence (mathematical logic)Inference Infinite-valued logic Infinite set Information theory Inhabited set Injective function Interior algebra Internet Archive Interpretation (logic)Interpretation (model theory)Interpretation function Intersection (set theory)Intuitionistic logic Irving Anellis Isomorphism Ivor Grattan-Guinness Jacques Riguet Johns Hopkins University Journal of Symbolic Logic János Bolyai Mathematical Society Kolmogorov complexity Kripke's theory of truth Kripke–Platek set theory Lambda calculus Large cardinal Lattice (order)Lecture Notes in Mathematics Leibniz operator Lemma (mathematics)Leopold Löwenheim Lindenbaum–Tarski algebra Lindström's theorem List of Hilbert systems List of axioms List of first-order theories List of formal systems List of mathematical theories List of set identities and relations List of statements independent of ZFC Logic Logic of relatives Logical biconditional Logical conjunction Logical connective Logical consequence Logical constant Logical disjunction Logical equality Logical equivalence Logical matrix Logical system Logical truth Logicism Louis Couturat Löwenheim–Skolem theorem MV-algebra Many-valued logic Map (mathematics)Material conditional Mathematical Association of America Mathematical logic Mathematical object Mathematics Matrix multiplication Metalanguage Metaphysics Minimal axioms for Boolean algebra Modal algebra Modal logic Model complete theory Model theory Modus ponens Monadic Boolean algebra Monadic predicate calculus Monadic predicate logic Monadic second-order logic Morse–Kelley set theory N. M. Ferrers NP (complexity)Nachlass Naive set theory Natural deduction Negation New Foundations Non-Euclidean geometry Non-classical logic Non-logical symbol Non-standard model Non-standard model of arithmetic Normal modal logic Open Court Publishing Company Open formula Operation (mathematics)Order theory Ordinal analysis Ordinal number Outer product P (complexity)P versus NP problem Paradoxes of set theory Partial function Partition of a set Peano arithmetic Peano axioms PhilPapers Philosophy Philosophy of mathematics Polyadic algebra Power set Predicate (mathematical logic)Predicate functor logic Predicate logic Predicate variable Presupposition Prime model Primitive notion Primitive recursive arithmetic Primitive recursive function Principia Mathematica Proof of impossibility Proof theory Proper extension Proposition Propositional calculus Propositional formula Propositional function Propositional variable Quantifier (logic)Quantifier rank Question Recursion Recursive set Relation (mathematics)Relation algebra Representation (mathematics)Representation theorem for Boolean algebras Reverse mathematics Robinson arithmetic Roger C. Lyndon Roger Maddux Rule of inference Russell's paradox S5 (modal logic)Satisfiability Saturated model Schröder–Bernstein theorem Second-order arithmetic Second-order logic Self-verifying theories Semantic theory of truth Semantics of logic Sentence (mathematical logic)Sentential logic Sequent calculus Set (mathematics)Set theory Signature (logic)Singleton (mathematics)Skolem arithmetic Socratic method Soundness Spectrum of a sentence Spectrum of a theory Square of opposition Stanford University Statement (logic)Stone duality Strength (mathematical logic)String (formal languages)Structure (mathematical logic)Studia Logica Substitution (logic)Substructure (mathematics)Supertask Surjective function Syllogism Symbol (formal)Symbolic logic Symbolical algebra Syntax (logic)T-schema Tarski's axiomatization of the reals Tarski's axioms Tarski's theory of truth Tarski's undefinability theorem Tarski–Grothendieck set theory Tautology (logic)Term (logic)Term logic Textbook The Principles of Mathematics Theorem Theories of truth Theory (mathematical logic)Thoralf Skolem Three-valued logic Timeline of mathematical logic Total relation Transfer principle Transitive set Transpose True arithmetic Truth predicate Truth table Truth value Turing machine Type (model theory)Type theory Ultrafilter (set theory)Ultraproduct Uncountable set Undecidable problem Uninterpreted function Union (set theory)Uniqueness quantification Universal algebra Universal quantification Universal set Universe (mathematics)Universe of discourse University of California, Berkeley University of California Press Urelement Validity (logic)Variable (mathematics)Vaughan Pratt Venn diagram Von Neumann universe Von Neumann–Bernays–Gödel set theory Well-formed formula Willard Quine ZFC Zermelo–Fraenkel set theory Łukasiewicz logic

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