New posts in foundations

How "Principia Mathematica" builds foundations

What formula of ZFC defines the set of natural numbers?

Is there a contradiction hiding in this alternative set theory with 3 axioms?

Uncountable closed set of reals biject with reals without replacement or choice

What of the "Sets, Classes, and Categories" approach to the foundations?

What is meant by "function" in the axiom schema of replacement.

Constructing a sequence up to infinity

Reference request: definition of class

Models of set theory

Why might Dieudonne have been "begging the question" by appealing to second-order Peano Axioms?

Why is something not a field if it's a proper class?

What precisely is lost when considering proper classes rather than sets?

Are there any foundations in which the universe itself gets dynamically extended?

Give a serious explanation of the difference between an equation and a function.

Founding Arithmetic on geometry

We need something more than the axioms of ZFC to prove the Dedekind completeness?

Why should the underlying set of a model be a set?

How strong is the axiom of well-ordered choice?

How is geometry defined using ZFC?

Does $\mathsf{ZFC} + \neg\mathrm{Con}(\mathsf{ZFC})$ suffice as a foundations of mathematics?