Stanley Tennenbaum
Encyclopedia
Stanley Tennenbaum was an American mathematician who contributed to the field of logic
. In 1959, he published Tennenbaum's theorem, which states that no countable
nonstandard model of Peano arithmetic
(PA) can be recursive
.
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
. In 1959, he published Tennenbaum's theorem, which states that no countable
Countable set
In mathematics, a countable set is a set with the same cardinality as some subset of the set of natural numbers. A set that is not countable is called uncountable. The term was originated by Georg Cantor...
nonstandard model of Peano arithmetic
Peano axioms
In mathematical logic, the Peano axioms, also known as the Dedekind–Peano axioms or the Peano postulates, are a set of axioms for the natural numbers presented by the 19th century Italian mathematician Giuseppe Peano...
(PA) can be recursive
Recursion theory
Computability theory, also called recursion theory, is a branch of mathematical logic that originated in the 1930s with the study of computable functions and Turing degrees. The field has grown to include the study of generalized computability and definability...
.
External links
- http://mamls.org/Tennenbaum