11 citations · 29 across the 6 of their papers we have counts for
7 papers
Reflection ranks via infinitary derivations
James Walsh
There is no infinite sequence of -sound extensions of each of which proves -reflection of the next. This engenders a well-founded ``reflection rankin…
On the hierarchy of natural theories
James Walsh
It is a well-known empirical phenomenon that natural axiomatic theories are pre-well-ordered by consistency strength. Without a precise mathematical definition of "natural," it is…
Reducing -model reflection to iterated syntactic reflection
Fedor Pakhomov, James Walsh
In mathematical logic there are two seemingly distinct kinds of principles called "reflection principles." Semantic reflection principles assert that if a formula holds in the whol…
Incompleteness and Jump Hierarchies
Patrick Lutz, James Walsh
This paper is an investigation of the relationship between Gödel's second incompleteness theorem and the well-foundedness of jump hierarchies. It follows from a classic theorem of…
A note on the consistency operator
James Walsh
It is a well known empirical observation that natural axiomatic theories are pre-well-ordered by consistency strength. For any natural theory , the next strongest natural theory…
Reflection ranks and ordinal analysis
Fedor Pakhomov, James Walsh
It is well-known that natural axiomatic theories are well-ordered by consistency strength. However, it is possible to construct descending chains of artificial theories with respec…
On the inevitability of the consistency operator
Antonio Montalbán, James Walsh
We examine recursive monotonic functions on the Lindenbaum algebra of . We prove that no such function sends every consistent to a sentence with deductive strength…