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 Logic of Cardinality Comparison Without the Axiom of Choice
Matthew Harrison-Trainor, Dhruv Kulshreshtha
We work in the setting of Zermelo-Fraenkel set theory without assuming the Axiom of Choice. We consider sets with the Boolean operations together with the additional structure of c…
The homeomorphisms of the SierpiÅski carpet are not classifiable by countable structures
Dhruv Kulshreshtha, Aristotelis Panagiotopoulos
We show that the homeomorphisms of the SierpiÅski carpet are not classifiable, up to conjugacy, using isomorphism types of countable structures as invariants.