All Questions

I'm interested in find out what were some of the first uses of mathematical induction in the literature. I am aware that in order to define addition and multiplication axiomatically, mathematical ...

Georges Reeb's "claim Q" is the statement that "naive integers don't fill up $\mathbb{N}$". To anyone familiar with model theory this could easily be interpreted as the existence of nonstandard models ...

I recently became interested in some problems concerning decidability of extensions of Presburger arithmetic. However, being a number-theorist rather than a logician, I am confused by some notational ...

On Wikipedia, there is a list of properties of sets of reals, which are in some sense "interesting": just have a look. I could not find a comparable list of properties of sets of natural numbers (...

I've relatively recently learned about Goodstein's Theorem and its unprovability in Peano arithmetic (the Kirby-Paris Theorem). I do not have any real knowledge of formal logic; but I think I've seen ...