12 citations · 66 across the 25 of their papers we have counts for
12 papers · 1 filter
Hyperreal differentiation with an idempotent ultrafilter
Samuel Allen Alexander, Bryan Dawson
In the hyperreals constructed using a free ultrafilter on R, where [f] is the hyperreal represented by f:R->R, it is tempting to define a derivative operator by [f]'=[f'], but unfo…
Strengthening Consistency Results in Modal Logic
Samuel Allen Alexander, Arthur Paul Pedersen
A fundamental question asked in modal logic is whether a given theory is consistent. But consistent with what? A typical way to address this question identifies a choice of backgro…
Formal differential variables and an abstract chain rule
Samuel Allen Alexander
One shortcoming of the chain rule is that it does not iterate: it gives the derivative of f(g(x)), but not (directly) the second or higher-order derivatives. We present iterated di…
Self-referential theories
Samuel Allen Alexander
We study the structure of families of theories in the language of arithmetic extended to allow these families to refer to one another and to themselves. If a theory contains schema…
Guessing, Mind-changing, and the Second Ambiguous Class
Samuel Alexander
In his dissertation, Wadge defined a notion of guessability on subsets of the Baire space and gave two characterizations of guessable sets. A set is guessable iff it is in the seco…
Fast-collapsing theories
Samuel Alexander
Reinhardt's conjecture, a formalization of the statement that a truthful knowing machine can know its own truthfulness and mechanicalness, was proved by Carlson using sophisticated…