4 papers
A Gentle Introduction to the Axiom of Choice
Andreas Blass, Dhruv Kulshreshtha
This article offers a gentle introduction to the axiom of choice. We introduce the axiom, discuss some common objections to it, and present three kinds of reasons to accept it. Alt…
A Reverse Mathematical Analysis of Hilbert's Nullstellensatz and Basis Theorem
Dhruv Kulshreshtha
This paper presents an expository reverse-mathematical analysis of two fundamental theorems in commutative algebra: Hilbert's Nullstellensatz and Basis Theorem. In addition to its…
The homeomorphisms of the Sierpiński carpet are not classifiable by countable structures
Dhruv Kulshreshtha, Aristotelis Panagiotopoulos
We show that the homeomorphisms of the Sierpiński carpet are not classifiable, up to conjugacy, using isomorphism types of countable structures as invariants.
Cardinal Well-foundedness and Choice
Andreas Blass, Dhruv Kulshreshtha
We consider several notions of well-foundedness of cardinals in the absence of the Axiom of Choice. Some of these have been conflated by some authors, but we separate them carefull…