Number theory and elementary arithmetic
By Jeremy Avigad. 2003
57 citations recorded by the source corpus.
Elementary arithmetic (also known as “elementary function arithmetic”) is a fragment of first-order arithmetic so weak that it cannot prove the totality of an iterated exponential function. Surprisingly, however, the theory turns out to be remarkably robust. I will discuss formal results that show that many theorems of number theory and combinatorics are derivable in elementary arithmetic, and try to place these results in a broader philosophical context.
Subfields: Algebra and Number Theory, Mathematical Physics, Theoretical Computer Science
View Paper: https://www.semanticscholar.org/paper/6ab9fa95e8e83cf48669a78ae1631eded4a8d65c
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Mathematical Physics
In Theoretical Computer Science
Citations in the corpus
- Proof Theory (2017, background): “Surprisingly, via coding of finitary objects as natural numbers, this system is expressive and strong enough to develop most portions of mathematics that involve only finite objects and structures [3].”
- Hilbert's program then and now (2005, background): “[ Avigad, 2003] gives an excellent survey of the issues and results related to this conjecture and places it in the philosophical context of Hilbert’s program.”