In logic, Richard's paradox is a semantical antinomy of set theory and natural language first described by the French mathematician Jules Richard in which year, Kurt Gödel specifically cites Richard's antinomy as a semantical analogue to his syntactical incompleteness result?
1905
Kurt Gödel
Kurt Friedrich Gödel ( , ; ] ; April 28, 1906 – January 14, 1978) was an Austrian, and later American, logician, mathematician, and philosopher.
 Considered along with Aristotle, Alfred Tarski and Gottlob Frege to be one of the most significant logicians in history, Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell, Alfred North Whitehead, and David Hilbert were analyzing the use of logic and set theory to understand the foundations of mathematics pioneered by Georg Cantor.
Richard's paradox
In logic, Richard's paradox is a semantical antinomy of set theory and natural language first described by the French mathematician Jules Richard in 1905.
 The paradox is ordinarily used to motivate the importance of distinguishing carefully between mathematics and metamathematics.
 Kurt Gödel specifically cites Richard's antinomy as a semantical analogue to his syntactical incompleteness result in the introductory section of "On Formally Undecidable Propositions in Principia Mathematica and Related Systems I".
 The paradox was also a motivation of the development of predicative mathematics.
Constructible universe
In mathematics, in set theory, the constructible universe (or Gödel's constructible universe), denoted L, is a particular class of sets that can be described entirely in terms of simpler sets.
 It was introduced by Kurt Gödel in his 1938 paper "The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis".
 In this, he proved that the constructible universe is an inner model of ZF set theory, and also that the axiom of choice and the generalized continuum hypothesis are true in the constructible universe.
 This shows that both propositions are consistent with the basic axioms of set theory, if ZF itself is consistent.
 Since many other theorems only hold in systems in which one or both of the propositions is true, their consistency is an important result. 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.
 These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics.
 The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible. Gödel numbering
In mathematical logic, a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Gödel number.
 The concept was used by Kurt Gödel for the proof of his incompleteness theorems.
 () Curry's paradox
Curry's paradox is a paradox in which an arbitrary claim F is proved from the mere existence of a sentence C that says of itself "If C, then F", requiring only a few apparently innocuous logical deduction rules.
 Since F is arbitrary, any logic having these rules proves everything.
 The paradox may be expressed in natural language and in various logics, including certain forms of set theory, lambda calculus, and combinatory logic. John W. Dawson Jr.
John W. Dawson Jr. (born February 4, 1944) is Professor of Mathematics, Emeritus at Pennsylvania State University at York.
 Born in Wichita, Kansas, he attended M.I.T. as a National Merit Scholar before earning a doctorate in mathematical logic from the University of Michigan in 1972.
 An internationally recognized authority on the life and work of Kurt Gödel, Professor Dawson is the author of numerous articles on axiomatic set theory and the history of modern logic.
 During the years 1982 to 1984, he catalogued Gödel's papers at the Institute for Advanced Study in Princeton, and afterward he served as a co-editor of Gödel's Collected Works.
 He recently retired as co-Editor-in-Chief of the journal "History and Philosophy of Logic". Ramified forcing
In the mathematical discipline of set theory, ramified forcing is the original form of forcing introduced by to prove the independence of the continuum hypothesis from Zermelo–Fraenkel set theory.
 Ramified forcing starts with a model M of set theory in which the axiom of constructibility, "V" = "L" , holds, and then builds up a larger model "M"["G"] of Zermelo–Fraenkel set theory by adding a generic subset G of a partially ordered set to M , imitating Kurt Gödel's constructible hierarchy. Morse–Kelley set theory
In the foundation of mathematics, Morse–Kelley set theory (MK), Kelley–Morse set theory (KM), Morse–Tarski set theory (MT), Quine–Morse set theory (QM) or the system of Quine and Morse is a first order axiomatic set theory that is closely related to von Neumann–Bernays–Gödel set theory (NBG).
 While von Neumann–Bernays–Gödel set theory restricts the bound variables in the schematic formula appearing in the axiom schema of Class Comprehension to range over sets alone, Morse–Kelley set theory allows these bound variables to range over proper classes as well as sets, as first suggested by Quine in 1940 for his system ML. Sy Friedman
Sy-David Friedman (born May 23, 1953 in Chicago) is an American and Austrian mathematician and a professor of mathematics at the University of Vienna and the director of the Kurt Gödel Research Center for Mathematical Logic.
 His main research interest lies in mathematical logic, in particular in set theory and recursion theory.