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pt: Alfred Tarski
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pt and Tarski
pt: Problema círculo-quadrado de Tarski
Alfred and Tarski
* Tarski's axioms: Alfred Tarski ( 1902 – 1983 ) and his students defined elementary Euclidean geometry as the geometry that can be expressed in first-order logic and does not depend on set theory for its logical basis, in contrast to Hilbert's axioms, which involve point sets.
* Alfred Tarski ( 1951 ) A Decision Method for Elementary Algebra and Geometry.
In a letter to Hayek in 1944, Popper stated, " I think I have learnt more from you than from any other living thinker, except perhaps Alfred Tarski.
* Jürgen Alex: Zum Einfluß elementarer Sätze der mathematischen Logik bei Alfred Tarski auf die drei Computerkonzepte des Konrad Zuse.
* Jürgen Alex: Zur Entstehung des Computers – von Alfred Tarski zu Konrad Zuse.
Alfred Tarski diagnosed the paradox as arising only in languages that are " semantically closed ", by which he meant a language in which it is possible for one sentence to predicate truth ( or falsehood ) of another sentence in the same language ( or even of itself ).
This result, known as Tarski's undefinability theorem, was discovered independently by Gödel ( when he was working on the proof of the incompleteness theorem ) and by Alfred Tarski.
* Alfred Tarski
Alfred Tarski explained the role of primitive notions as follows:
* Alfred Tarski ( 1946 ) Introduction to Logic and the Methodology of the Deductive Sciences, page 118, Oxford University Press.
He then goes on to cite, as an example, a 1930 paper he wrote with Alfred Tarski on the sentential calculus.
Among the philosophers who grappled with this problem is Alfred Tarski, whose semantic theory is summarized further below in this article.
Logician and philosopher Alfred Tarski developed the theory for formal languages ( such as formal logic ).
** Alfred Tarski, Polish logician and mathematician ( died 1983 )
Later, Jan Łukasiewicz and Alfred Tarski together formulated a logic on n truth values where n ≥ 2.
* Alfred Tarski ( 1946 ) Introduction to Logic and to the Methodology of Deductive Sciences, republished 1995 by Dover Publications, Inc., New York, NY ISBN 0-486-28462-X
Developments in metamathematics and category theory in the 1940s and 1950s furthered the field, particularly the work of Abraham Robinson, Alfred Tarski, Andrzej Mostowski, and their students ( Brainerd 1967 ).
Moreover, with Alfred Tarski and Wacław Sierpiński he provided most of the theory concerning Polish spaces ( that are indeed named after these mathematicians and their legacy ).
Other formalists, such as Rudolf Carnap, Alfred Tarski and Haskell Curry, considered mathematics to be the investigation of formal axiom systems.
In his 1975 article " Outline of a Theory of Truth ", Kripke showed that a language can consistently contain its own truth predicate, which was deemed impossible by Alfred Tarski, a pioneer in the area of formal theories of truth.
Sets his theory of truth ( against Alfred Tarski ), where an object language can contain its own truth predicate.
This result, known as Tarski's undefinability theorem, was discovered independently by Gödel ( when he was working on the proof of the incompleteness theorem ) and by Alfred Tarski.
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