Tennenbaum's theorem, named for Stanley Tennenbaum who presented the theorem in 1959, is a result in mathematical logic that states that no countable nonstandard...

formulas), then Tennenbaum's theorem shows that it has no recursive non-standard models. The completeness theorem and the compactness theorem are two cornerstones...

Stanley Tennenbaum (April 11, 1927 – May 4, 2005) was an American mathematician who contributed to the field of logic. In 1959, he published Tennenbaum's theorem...

(modal logic) Soundness theorem (mathematical logic) Tarski's indefinability theorem (mathematical logic) Tennenbaum's theorem (model theory) Uncountability...

explicit construction of such a nonstandard model. On the other hand, Tennenbaum's theorem, proved in 1959, shows that there is no countable nonstandard model...

of all infinite cardinalities. However, unlike Peano arithmetic, Tennenbaum's theorem does not apply to Q, and it has computable non-standard models. For...

structure of the rationals. There is more to it than that though: Tennenbaum's theorem shows that for any countable non-standard model of Peano arithmetic...

square with sides of one unit of length; this follows from the Pythagorean theorem. It was probably the first number known to be irrational. The fraction...

\Sigma _{1}} is categorical. Categoricity here is reminiscent of Tennenbaum's theorem. The model validates H A {\displaystyle {\mathsf {HA}}} but not P...

from the axioms of ZFC. In 1931, Kurt Gödel proved his incompleteness theorems, establishing that many mathematical theories, including ZFC, cannot prove...

of the standard axiomatic system of set theory known as ZFC; Solovay & Tennenbaum (1971) showed that the statement can neither be proven nor disproven from...

a dissertation on A Functorial Form of the Differentiable Riemann–Roch theorem. Solovay has spent his career at the University of California at Berkeley...

equisingularity theory. Some of his major results, Zariski's main theorem and the Zariski theorem on holomorphic functions, were amongst the results generalized...

not collapsed. This is often accomplished by the use of a preservation theorem such as: Finite support iteration of c.c.c. forcings (see countable chain...

Leopold Löwenheim publishes a proof of the (downward) Löwenheim-Skolem theorem, implicitly using the axiom of choice. 1918 - C. I. Lewis writes A Survey...

Robert Soare and Carl Jockusch to prove, among other results, the low basis theorem. Here P is the set of nonempty Π 1 0 {\displaystyle \Pi _{1}^{0}} subsets...