Alfred Tarski and undecidable theories
نویسندگان
چکیده
منابع مشابه
Alfred Tarski . Life and Logic Reviewed by Hourya Benis Sinaceur
Alfred Tarski (1901–1983) is one of the two greatest logicians of the twentieth century, the other being Kurt Gödel (1906–1978). Each began his career in Europe, respectively in Warsaw and Vienna, and came to America shortly before the Second World War. In contrast to the otherworldly Gödel, Tarski was ambitious and practical. He strove for, and succeeded at, building a school of logic at the U...
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Suppose that T is an equational theory of groups or of rings. If T is finitely axiomatizable, then there is a least number μ so that T can be axiomatized by μ equations. This μ can depend on the operation symbols that occur in T . In the 1960’s, Alfred Tarski and Thomas C. Green completely determined the values of μ for arbitrary equational theories of groups and of rings. While Tarski and Gree...
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We introduce a general framework to prove undecidability of fragments. This is applied to fragments of theories arising in algebra and recursion theory. For instance, the V3V-theories of the class of finite distributive lattices and of the p.o. of recursively enumerable many-one degrees are shown to be undecidable.
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1 Diophantine undecidability Let T be a theory in the usual rst-order language of arithmetic L A (with non-logical symbols 0; 1; +; ; <) extending PA ? , the theory of the nonnegative parts of discretely ordered rings. I shall make use of the usual classes of L A-formulas deened in terms of quantiier complexity, 9 1 1 is the set of L A-formulas of the form 9 x (x; y) with quantiier-free, and 1 ...
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 1986
ISSN: 0022-4812,1943-5886
DOI: 10.2307/2273902