1 citations · 1 across the 6 of their papers we have counts for
7 papers
Stalnaker's logical problem of conditionals is unsolvable
Alexander W. Kocurek, James Walsh, Yale Weiss
The logical problem of conditionals, as conceived by Stalnaker, amounts to axiomatizing a particular semantics for conditionals which utilizes selection functions that take proposi…
Incompleteness in Quantified Conditional Logic
Alexander W. Kocurek, James Walsh, Yale Weiss
Stalnaker and Thomason famously proved that the conditional logic \textsf{C2} with first-order quantifiers is complete with respect to a selection function semantics. However, the…
Descending sequences in reflection hierarchies
Mateusz Łełyk, James Walsh
There is no recursively enumerable sequence of sufficiently strong 2-consistent r.e. theories such that each proves the -consistency of the next. Montalbán and Shavrukov indepen…
Ranking theories via encoded -models
Hanul Jeon, Patrick Lutz, Fedor Pakhomov +1
Ranking theories according to their strength is a recurring motif in mathematical logic. We introduce a new ranking of arbitrary (not necessarily recursively axiomatized) theories…
A classification of incompleteness statements
Henry Towsner, James Walsh
For which choices of does no sufficiently strong -sound and -definable extension theory prove its own -soundness? We give a complete answer, ther…
Modal definability in Kripke's theory of truth
James Walsh
In Outline of a Theory of Truth, Kripke introduces some of the central concepts of the logical study of truth and paradox. He informally defines some of these -- such as groundedne…
Generalized ordinal analysis and reflection principles in set theory
Hanul Jeon, James Walsh
It is widely claimed that the natural axiom systems$\unicode{x2013}$including the large cardinal axioms$\unicode{x2013}$form a well-ordered hierarchy. Yet, as is well-known, it is…