Logic and Foundations

Typically, a logic consists of a formal or informal language together with a deductive system and/or a model-theoretic semantics.

Every set is smaller than its power set

In mathematics, specifically set theory, the continuum hypothesis (abbreviated CH) is a hypothesis

In the field of mathematical logic, a clear distinction is made between two notions of axioms: logical and non-logical.

However, it demonstrates a general technique that has since been used in a wide range of proofs, including the first of Gödel's incompleteness theorems and Turing's answer to the Entscheidungsproblem.

The P = NP problem can also be stated as a question about expressive power in descriptive complexity.

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories.

In the philosophy of mathematics, the abstraction of actual infinity

Foundations of mathematics are the logical and mathematical frameworks that allow the development of mathematics without generating self-contradictory theories, and to have reliable concepts of theorems, proofs, algorithms, etc.

known for his work in mathematical logic

In his early career Whitehead wrote primarily on mathematics, logic, and physics.

Quine's research was mainly on logic although always with a philosophical motivation

worked in both analysis, especially measure theory, and in the foundations of mathematics

was an American logician and mathematician

mathematical logic, Abelian group theory

was a Polish mathematician and logician

His work centred on philosophical logic, mathematical logic and history of logic.

Ernst Schröder was a German mathematician who did important work is in the area of algebra, set theory and logic.

Christine Ladd-Franklin was an American psychologist, logician and mathematician

Giuseppe Peano was the founder of symbolic logic and his interests centred on the foundations of mathematics

He was the French advocate of the symbolic logic that emerged in the years before World War I

She is best known for her efforts in restoring the research of mathematical logic in the Soviet Union

made major contributions to logic, such as theories of relations and quantification

He was a logical positivist, and a member of the Vienna Circle.

for the univalent foundations of mathematics and homotopy type theory

was a Russian/Soviet logician and theoretician of electrical engineering

is a retired American logician

Clavius, (25 March 1538-6 February 1612) was a Jesuit German mathematician and physicist, head of mathematicians at the Collegio Romano, and astronomer who was a member of the Vatican commission that accepted the proposed calendar invented by

He was a mathematician and logician, and wrote an influential book on the origin of languages. == Life == He was son of Robert Brerewood, a wetglover, three times mayor of Chester, and was born and educated there at The King's School.

Petrus Ramus (French: Pierre de La Ramée; Anglicized as Peter Ramus ; 1515-26 August 1572) was a French humanist, logician, and educational reformer.

He was a precursor of the Renaissance Scientific Revolution and investigated the relationships between mathematics, logic and philosophy.

Joachim Jungius (born Joachim Junge; 22 October 1587-23 September 1657) was a German mathematician, logician and philosopher of science. == Life == Jungius was a native of Lübeck.

Popular record for Arnauld's penetration was much increased in his L'Art de penser, commonly known as the Port-Royal Logic, which kept its place as an elementary text-book until the 20th century and is considered a paradigmatical work of term logic.

In 1811 he published his System der Logik

was a Spanish philosopher and Jesuit, considered a pioneer in the fields of combinatorics and mathematical logic.

was an American logician who worked in the field of computational neuroscience

In his studies of mathematical logic Ockham made important contributions to it which are significant today

made contributions to mathematical logic and the philosophy of language

was an American philosopher and a mathematical logician who taught at the Massachusetts Institute of Technology

a form of arithmetic in which one allows induction but removes multiplication, to obtain a decidable theory

He performed research in the field of set theory and predicate logic.

In mathematical logic, Martin-Löf has been active in developing intuitionistic type theory as a constructive foundation of mathematics

He developed constructive logic, constructive type theory and constructive analysis.

Matematička logika 1964.

German philosopher and mathematician known for his contributions to logic and physics

he specializes in logic and philosophy of mathematics

was an American logician, whose works played a strong role in the development of logic

he supported a conventionalist thesis on the foundation of mathematics

a PhD dissertation on the development of arithmetic in axiomatic set theory

In computer science and mathematical logic the Turing degree (named after Alan Turing) or degree of unsolvability of a set of natu

nt consistency theorem is an important theorem of mathematical logic.

In mathematical logic, a theory is categorical if it has exactly one model (up to isomorphism).

In mathematical logic and computer science, Gabbay's separation theorem states that any formula in linear temporal logic (LTL) wit

In mathematical logic, a deduction theorem is a metatheorem that justifies doing conditional proofs from a hypothesis in systems t

In mathematical logic, a theory can be extended with new constants or function names under certain conditions with assurance that

In modal logic, Sahlqvist formulas are a certain kind of modal formula with remarkable properties.

In logic, soundness can refer to either a property of arguments or a property of formal deductive systems.

In logic, mathematics, and computer science, arity ( ) is the number of arguments or operands taken by a function, operation or re

In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition P to another propo

In mathematical logic, a sequent is a very general kind of conditional assertion.

In quantified modal logic, the Barcan formula and the converse Barcan formula (more accurately, schemata rather than formulas) (i)

In mathematical logic, Craig's interpolation theorem is a result about the relationship between different logical theories.

In mathematical logic, the Beth definability theorem is a fundamental result in logic that states a property implicitly defined by

In mathematical logic, an omega-categorical theory is a theory that has exactly one countably infinite model up to isomorphism.

In mathematical logic, a formula is said to be absolute to some class of structures (also called models), if it has the same truth

ph property definable in the monadic second-order logic of graphs can be decided in linear time on graphs of bounded treewidth.

In mathematical logic, the diagonal lemma (also known as diagonalization lemma, self-reference lemma or fixed point theorem) estab

In metalogic and metamathematics, Frege's theorem is a metatheorem that states that the Peano axioms of arithmetic can be derived

In mathematical logic, the Barwise compactness theorem, named after Jon Barwise, is a generalization of the usual compactness theo

In mathematical logic and computer science, Kamp's theorem states that linear temporal logic is equivalent to the monadic first-or

In mathematical logic, Goodstein's theorem is a statement about the natural numbers, proved by Reuben Goodstein in 1944, which sta

who presented the theorem in 1959, is a result in mathematical logic that states that no countable nonstandard model of first-orde

mathematical logic

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foundations of mathematics

mathematical logic

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Curry is best known for his work in combinatory logic.

known for the invention of combinatory logic

is an Israeli logician

Goodstein's theorem was among the earliest examples of theorems found to be unprovable in Peano arithmetic

best known for his work in mathematical logic

who worked in the field of foundations and mathematical logic

Evert Willem Beth (7 July 1908-12 April 1964) was a Dutch philosopher and logician, whose work principally concerned the foundations of mathematics.

George Boole ( BOOL; 2 November 1815-8 December 1864) was an English mathematician and philosopher often credited with revolutionizing logic by transforming it from a philosophical study of language into a mathematical system of algebraic equations using binary values and logical operators.

John Barkley Rosser Sr. (December 6, 1907, September 5, 1989) was an American logician, a student of Alonzo Church, and known for his part in the Church-Rosser theorem in lambda calculus.

Leopold Löwenheim [ˈle:o:pɔl̩d ˈlø:vɛnhaɪm] (26 June 1878 in Krefeld, 5 May 1957 in Berlin) was a German mathematician doing work in mathematical logic.

Per "Pelle" Lindström (9 April 1936-21 August 2009, Gothenburg) was a Swedish logician, after whom Lindström's theorem and the Lindström quantifier are named. (He also independently discovered Ehrenfeucht-Fraïssé games.) He was one of the key followers of Lars Svenonius.

Bernard Bolzano (UK: , US: ; German: [bɔlˈtsaːno]; Italian: [bolˈtsaːno]; born Bernardus Placidus Johann Nepomuk Bolzano; 5 October 1781-18 December 1848) was a Bohemian mathematician, logician, philosopher, theologian and Catholic priest of Italian extraction, also known for his liberal views.

Kenneth Jon Barwise (; June 29, 1942, March 5, 2000) was an American mathematician, philosopher, and logician who proposed some fundamental revisions to the way that logic is understood and used.

Ernst Friedrich Ferdinand Zermelo (; German: [tsɛɐ̯ˈmeːlo]; 27 July 1871-21 May 1953) was a German logician and mathematician, whose work has major implications for the foundations of mathematics.

The B, C, K, W system is a variant of combinatory logic that takes as primitive the combinators B, C, K, and W.

The SKI combinator calculus is a combinatory logic system and a computational system.

In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs.

Foundations of Mathematics Theorem Proving

Foundations of Mathematics Logic

Foundations of Mathematics Logic

Foundations of Mathematics Logic

Foundations of Mathematics Logic

Foundations of Mathematics Theorem Proving

Foundations of Mathematics Theorem Proving

Foundations of Mathematics Theorem Proving

Foundations of Mathematics Logic

computer science, the Entscheidungsproblem (German for 'decision problem'; pronounced [ɛntˈʃaɪ̯dʊŋspʁoˌbleːm]) is a challenge

In mathematics, an impossibility theorem is a theorem that demonstrates a problem or general set of problems cannot be solved. These are also known as proofs of impossibility

Foundations of Mathematics Logic

He introduced De Morgan's laws and his greatest contribution is as a reformer of mathematical logic.

Edward Nelson was an American mathematician who won the Steele Prize for applying probability to quantum field theory. He wrote several classic texts on the topic. In the latter part of his career he studied mathematical logic.

Gottlob Frege was a German mathematician who was one of the founders of modern symbolic logic putting forward the view that mathematics is reducible to logic.

Jacques Herbrand was a French mathematician who died young but made contributions to mathematical logic.

John Venn was an English mathematician and logician best known for the Venn diagrams which can be used to visualise the unions and intersections of sets.

As a mathematical logician, he was interested in increasing understanding by treating it as a game.

Moritz Pasch was a German mathematician who worked on the foundations of geometry. He found a number of assumptions in Euclid that nobody had noticed before.

Alonzo Church made important contributions to mathematical logic and theoretical computer science.