All Questions

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 ...

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 ...

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'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 ...

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 (...