2 citations · 3 across the 4 of their papers we have counts for
5 papers
Characterizations of ordinal analysis
James Walsh
Ordinal analysis is a research program wherein recursive ordinals are assigned to axiomatic theories. According to conventional wisdom, ordinal analysis measures the strength of th…
Evitable iterates of the consistency operator
James Walsh
Let's fix a reasonable subsystem of arithmetic; why are natural extensions of pre-well-ordered by consistency strength? In previous work, an approach to this question was p…
A robust proof-theoretic well-ordering
James Walsh
It is well-known that natural axiomatic theories are pre-well-ordered by logical strength, according to various characterizations of logical strength such as consistency strength a…
A characterization of ordinal analysis
James Walsh
Ordinal analysis induces a partition of -definable and -sound theories whereby two theories are equivalent if they have the same proof-theoretic ordinal. We show that…
An incompleteness theorem via ordinal analysis
James Walsh
We present an analogue of Gödel's second incompleteness theorem for systems of second-order arithmetic. Whereas Gödel showed that sufficiently strong theories that are -soun…