Stanley Tennenbaum (April 11, 1927 – May 4, 2005) was an American mathematician who contributed to the field of

logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...

. In 1959, he published Tennenbaum's theorem, which states that no

countable In mathematics, a Set (mathematics), set is countable if either it is finite set, finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is ''countable'' if there exists an injective function fro ...

nonstandard model In model theory, a discipline within mathematical logic, a non-standard model is a model of a theory that is not isomorphic to the intended model (or standard model).Roman Kossak, 2004 ''Nonstandard Models of Arithmetic and Set Theory'' American M ...

Peano arithmetic In mathematical logic, the Peano axioms (, ), also known as the Dedekind–Peano axioms or the Peano postulates, are axioms for the natural numbers presented by the 19th-century Italian mathematician Giuseppe Peano. These axioms have been used nea ...

(PA) can be

recursive Recursion occurs when the definition of a concept or process depends on a simpler or previous version of itself. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in m ...

, i.e. the operations + and × of a nonstandard model of PA are not recursively definable in the + and × operations of the standard model. He was a professor at

Yeshiva University Yeshiva University is a Private university, private Modern Orthodox Judaism, Orthodox Jewish university with four campuses in New York City.

in the 1960s.

References

External links

Historical Remarks on Suslin's Problem
Article by

Akihiro Kanamori is a Japanese-born American mathematician. He specializes in set theory and is the author of the monograph on large cardinals, '' The Higher Infinite''. He has written several essays on the history of mathematics, especially set theory. Kanamor ...

describing some of Tennenbaum's work, with some biographical info. 1927 births 2005 deaths 20th-century American mathematicians 21st-century American mathematicians {{US-mathematician-stub