223 citations · 725 across the 95 of their papers we have counts for
107 papers
Class choice and the surprising weakness of Kelley-Morse set theory
Victoria Gitman, Joel David Hamkins, Thomas A. Johnstone
Kelley-Morse set theory KM is weaker than generally supposed and fails to prove several principles that may be desirable in a foundational second-order set theory. Even though KM i…
A potentialist conception of ultrafinitism
Joel David Hamkins
I shall explore various senses in which ultrafinitism can be fruitfully understood as engaging with a potentialist perspective in mathematics. First, I explain that every model …
How the continuum hypothesis could have been a fundamental axiom
Joel David Hamkins
I describe a simple historical thought experiment showing how we might have come to view the continuum hypothesis as a fundamental axiom, one necessary for mathematics, indispensab…
Did Turing prove the undecidability of the halting problem?
Joel David Hamkins, Theodor Nenu
We discuss the accuracy of the attribution commonly given to Turing's 1936 paper "On computable numbers..." for the computable undecidability of the halting problem, coming eventua…
Pseudo-countable models
Joel David Hamkins
Every mathematical structure has an elementary extension to a pseudo-countable structure, one that is seen as countable inside a suitable class model of set theory, even though it…
Fregean abstraction in Zermelo-Fraenkel set theory: a deflationary account
Joel David Hamkins
The standard treatment of sets and definable classes in first-order Zermelo-Fraenkel set theory accords in many respects with the Fregean foundational framework, such as the distin…