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 science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premise ...

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

countable In mathematics, a set is countable if either it is 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 from it into the natural numbers ...

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 Ma ...

of Peano arithmetic (PA) can be

recursive Recursion (adjective: ''recursive'') occurs when a thing is defined in terms of itself or of its type. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics ...

, 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 Orthodox Jewish university with four campuses in New York City."About YU
on the Yeshiva Universi ...

in the 1960s.

References

External links

Historical Remarks on Suslin's Problem
Article by Akihiro Kanamori 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