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21 relations: Andrey Kolmogorov, Arend Heyting, Bottom type, Computable function, Constructivism (mathematics), Formal system, Gödel's incompleteness theorems, Heyting arithmetic, Intuitionistic logic, L. E. J. Brouwer, Lambda calculus, Law of excluded middle, Law of noncontradiction, Mathematical induction, Mathematical logic, Peano axioms, Principle of explosion, Realizability, Stephen Cole Kleene, Structural induction, Well-formed formula.
Andrey Kolmogorov
Andrey Nikolaevich Kolmogorov (a, 25 April 1903 – 20 October 1987) was a 20th-century Soviet mathematician who made significant contributions to the mathematics of probability theory, topology, intuitionistic logic, turbulence, classical mechanics, algorithmic information theory and computational complexity.
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Arend Heyting
__notoc__ Arend Heyting (9 May 1898 – 9 July 1980) was a Dutch mathematician and logician.
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Bottom type
In type theory, a theory within mathematical logic, the bottom type is the type that has no values.
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Computable function
Computable functions are the basic objects of study in computability theory.
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Constructivism (mathematics)
In the philosophy of mathematics, constructivism asserts that it is necessary to find (or "construct") a mathematical object to prove that it exists.
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Formal system
A formal system is the name of a logic system usually defined in the mathematical way.
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Gödel's incompleteness theorems
Gödel's incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system containing basic arithmetic.
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Heyting arithmetic
In mathematical logic, Heyting arithmetic (sometimes abbreviated HA) is an axiomatization of arithmetic in accordance with the philosophy of intuitionism (Troelstra 1973:18).
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Intuitionistic logic
Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof.
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L. E. J. Brouwer
Luitzen Egbertus Jan Brouwer (27 February 1881 – 2 December 1966), usually cited as L. E. J. Brouwer but known to his friends as Bertus, was a Dutch mathematician and philosopher, who worked in topology, set theory, measure theory and complex analysis.
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Lambda calculus
Lambda calculus (also written as λ-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution.
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Law of excluded middle
In logic, the law of excluded middle (or the principle of excluded middle) states that for any proposition, either that proposition is true or its negation is true.
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Law of noncontradiction
In classical logic, the law of non-contradiction (LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory statements cannot both be true in the same sense at the same time, e.g. the two propositions "A is B" and "A is not B" are mutually exclusive.
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Mathematical induction
Mathematical induction is a mathematical proof technique.
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Mathematical logic
Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.
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Peano axioms
In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano.
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Principle of explosion
The principle of explosion (Latin: ex falso (sequitur) quodlibet (EFQ), "from falsehood, anything (follows)", or ex contradictione (sequitur) quodlibet (ECQ), "from contradiction, anything (follows)"), or the principle of Pseudo-Scotus, is the law of classical logic, intuitionistic logic and similar logical systems, according to which any statement can be proven from a contradiction.
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Realizability
In mathematical logic, realizability is a collection of methods in proof theory used to study constructive proofs and extract additional information from them.
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Stephen Cole Kleene
Stephen Cole Kleene (January 5, 1909 – January 25, 1994) was an American mathematician.
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Structural induction
Structural induction is a proof method that is used in mathematical logic (e.g., in the proof of Łoś' theorem), computer science, graph theory, and some other mathematical fields.
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Well-formed formula
In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet that is part of a formal language.
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References
[1] https://en.wikipedia.org/wiki/Brouwer–Heyting–Kolmogorov_interpretation
