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.
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.
In mathematical logic, a first-order Gödel logic is a member of a family of finite- or infinite-valued logics in which the sets of truth values "V" are closed subsets of the interval [0,1] containing both 0 and 1.
 Different such sets "V" in general determine different Gödel logics.
 The concept is named after Kurt Gödel.
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".
In mathematical logic, Rosser's trick is a method for proving Gödel's incompleteness theorems without the assumption that the theory being considered is ω-consistent (Smorynski 1977, p. 840; Mendelson 1977, p. 160).
 This method was introduced by J. Barkley Rosser in 1936, as an improvement of Gödel's original proof of the incompleteness theorems that was published in 1931.
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.
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In proof theory, a discipline within mathematical logic, double-negation translation, sometimes called negative translation, is a general approach for embedding classical logic into intuitionistic logic, typically by translating formulas to formulas which are classically equivalent but intuitionistically inequivalent.
 Particular instances of double-negation translation include Glivenko's translation for propositional logic, and the Gödel–Gentzen translation and Kuroda's translation for first-order logic.
Gödel is a declarative, general-purpose programming language that adheres to the logic programming paradigm.
 It is a strongly typed language, the type system being based on many-sorted logic with parametric polymorphism.
 It is named after logician Kurt Gödel.
Sir Michael Anthony Eardley Dummett, FBA (27 June 192527 December 2011) was a British philosopher, described as "among the most significant British philosophers of the last century and a leading campaigner for racial tolerance and equality."
 He was, until 1992, Wykeham Professor of Logic at the University of Oxford.
 He wrote on the history of analytic philosophy, most notably as an interpreter of Frege, and has made original contributions to the subject, particularly in the philosophies of mathematics, logic, language and metaphysics.
 He was known for his work on truth and meaning and their implications for the debates between realism and anti-realism, a term he helped popularize.
 He devised the Quota Borda system of proportional voting, based on the Borda count.
 In mathematical logic, he developed an intermediate logic, already studied by Kurt Gödel: the so-called Gödel–Dummett logic.
In mathematical logic and set theory, an ordinal notation is a partial function from the set of all finite sequences of symbols from a finite alphabet to a countable set of ordinals, and a Gödel numbering is a function from the set of well-formed formulae (a well-formed formula is a finite sequence of symbols on which the ordinal notation function is defined) of some formal language to the natural numbers.
 This associates each wff with a unique natural number, called its Gödel number.
 If a Gödel numbering is fixed, then the subset relation on the ordinals induces an ordering on well-formed formulae which in turn induces a well-ordering on the subset of natural numbers.
 A recursive ordinal notation must satisfy the following two additional properties:

Question: What is the original nationality of the namesake of Gödel logic?
Answer: Austrian