Articles of reverse math

Why is bounded induction stronger than open induction?

It seems to me that any formula in the language of first-order arithmetic which has only bounded quantifiers can be written as a formula without any quantifiers. For instance, “There exists an n < 1000 such that P(n)” can be written as “P(1) or P(2) or … or P(999)”, and “for all n < 100, […]

Relationship between l'Hospital's rule and the least upper bound property.

Statement of L’Hospital’s Rule Let $F$ be an ordered field. L’Hospital’s Rule. Let $f$ and $g$ be $F$-valued functions defined on an open interval $I$ in $F$. Let $c$ be an endpoint of $I$. Note $c$ may be a finite number or one of the symbols $-\infty$,$+\infty$. Suppose $f'(x)$ and $g'(x)$ are defined everywhere on […]

Is most of mathematics independent of set theory?

Is most of mathematics independent of set theory? Reading this quote by Noah Schweber: most of the time in the mathematical literature, we’re not even dealing with sets! it seems that the answer to my question is “yes”. But why? When I read in the mathematical literature, sets appear everywhere – we need them in […]

Constructiveness of Proof of Gödel's Completeness Theorem

As a mathematician interested in novel applications I am trying to gain a deeper understanding of (the non-constructiveness of) Gödel’s Completeness Theorem and have recently studying two texts: Mathematical Logic for Mathematicians (by Y.Manin) and the book on Reverse Mathematics by Simpson [2009]. Having read Mendelsohn and Crossley (and other works) I am actually surprised […]