4 papers
Foundations with Imagination
Toby Meadows
We show that countable set theory, , is unable to eliminate imaginaries. In other words, this theory cannot provide representatives for arbitrary defi…
Found in Translation: at the limits of the Hudetz program
Toby Meadows
This paper aims to provide an analysis of what it means when we say that a pair of theories, very generously construed, are equivalent in the sense that they are interdefinable. Wi…
Internal Categoricity and the Generic Multiverse
Toby Meadows
John Steel's theory, MV, of the generic multiverse provides a foundation for mathematics that aims to neutralize the effects of incompleteness brought on by forcing arguments. Jouk…
Teasing apart definitional equivalence
Jason Chen, Toby Meadows
In a recent paper, Enayat and Le lyk [2024] show that second order arithmetic and countable set theory are not definitionally equivalent. It is well known that these theories are b…