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28 relations: Abraham Robinson, Augustin-Louis Cauchy, Axiom of choice, Axiom schema of replacement, Axiom schema of specification, Conservative extension, Consistency, Definable real number, Edward Nelson, Finitism, First-order logic, Georg Cantor, Gottfried Wilhelm Leibniz, Great circle, Infinitesimal, Johann Bernoulli, Karel Hrbáček, Karl Weierstrass, Leonhard Euler, Logic, Model theory, Non-Euclidean geometry, Non-standard analysis, Real number, Richard Dedekind, Set (mathematics), Signature (logic), Zermelo–Fraenkel set theory.
Abraham Robinson
Abraham Robinson (born Robinsohn; October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of non-standard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were reincorporated into modern mathematics.
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Augustin-Louis Cauchy
Baron Augustin-Louis Cauchy FRS FRSE (21 August 178923 May 1857) was a French mathematician, engineer and physicist who made pioneering contributions to several branches of mathematics, including: mathematical analysis and continuum mechanics.
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Axiom of choice
In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that the Cartesian product of a collection of non-empty sets is non-empty.
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Axiom schema of replacement
In set theory, the axiom schema of replacement is a schema of axioms in Zermelo–Fraenkel set theory (ZF) that asserts that the image of any set under any definable mapping is also a set.
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Axiom schema of specification
In many popular versions of axiomatic set theory the axiom schema of specification, also known as the axiom schema of separation, subset axiom scheme or axiom schema of restricted comprehension is an axiom schema.
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Conservative extension
In mathematical logic, a conservative extension is a supertheory of a theory which is often convenient for proving theorems, but proves no new theorems about the language of the original theory.
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Consistency
In classical deductive logic, a consistent theory is one that does not contain a contradiction.
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Definable real number
Informally, a definable real number is a real number that can be uniquely specified by its description.
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Edward Nelson
Edward Nelson (May 4, 1932 – September 10, 2014) was a professor in the Mathematics Department at Princeton University.
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Finitism
Finitism is a philosophy of mathematics that accepts the existence only of finite mathematical objects.
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First-order logic
First-order logic—also known as first-order predicate calculus and predicate logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.
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Georg Cantor
Georg Ferdinand Ludwig Philipp Cantor (– January 6, 1918) was a German mathematician.
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Gottfried Wilhelm Leibniz
Gottfried Wilhelm (von) Leibniz (or; Leibnitz; – 14 November 1716) was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy.
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Great circle
A great circle, also known as an orthodrome, of a sphere is the intersection of the sphere and a plane that passes through the center point of the sphere.
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Infinitesimal
In mathematics, infinitesimals are things so small that there is no way to measure them.
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Johann Bernoulli
Johann Bernoulli (also known as Jean or John; – 1 January 1748) was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family.
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Karel Hrbáček
Karel Hrbáček (born 1944) is professor emeritus of mathematics at City College of New York.
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Karl Weierstrass
Karl Theodor Wilhelm Weierstrass (Weierstraß; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern analysis".
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Leonhard Euler
Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.
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Logic
Logic (from the logikḗ), originally meaning "the word" or "what is spoken", but coming to mean "thought" or "reason", is a subject concerned with the most general laws of truth, and is now generally held to consist of the systematic study of the form of valid inference.
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Model theory
In mathematics, model theory is the study of classes of mathematical structures (e.g. groups, fields, graphs, universes of set theory) from the perspective of mathematical logic.
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Non-Euclidean geometry
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those specifying Euclidean geometry.
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Non-standard analysis
The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Richard Dedekind
Julius Wilhelm Richard Dedekind (6 October 1831 – 12 February 1916) was a German mathematician who made important contributions to abstract algebra (particularly ring theory), axiomatic foundation for the natural numbers, algebraic number theory and the definition of the real numbers.
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Set (mathematics)
In mathematics, a set is a collection of distinct objects, considered as an object in its own right.
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Signature (logic)
In logic, especially mathematical logic, a signature lists and describes the non-logical symbols of a formal language.
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Zermelo–Fraenkel set theory
In mathematics, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox.
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Internal Set Theory, Internal Set theory.
References
[1] https://en.wikipedia.org/wiki/Internal_set_theory
