32 citations · 77 across the 6 of their papers we have counts for
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The generalized quantifiers of natural language are predicatively definable
Sean Walsh
This paper studies the definability of natural language generalized quantifiers. The semantics of generalized quantifiers are provided by a collection of subsets of the underlying…
Definability Aspects of the Denjoy Integral
Sean Walsh
The Denjoy integral is an integral that extends the Lebesgue integral and can integrate any derivative. In this paper, it is shown that the graph of the indefinite Denjoy integral…
Realizability Semantics for Quantified Modal Logic: Generalizing Flagg's 1985 Construction
Benjamin G. Rin, Sean Walsh
A semantics for quantified modal logic is presented that is based on Kleene's notion of realizability. This semantics generalizes Flagg's 1985 construction of a model of a modal ve…
Predicativity, the Russell-Myhill Paradox, and Church's Intensional Logic
Sean Walsh
This paper sets out a predicative response to the Russell-Myhill paradox of propositions within the framework of Church's intensional logic. A predicative response places restricti…
Relative Categoricity and Abstraction Principles
Sean Walsh, Sean Ebels-Duggan
Many recent writers in the philosophy of mathematics have put great weight on the relative categoricity of the traditional axiomatizations of our foundational theories of arithmeti…
Comparing Hume's Principle, Basic Law V and Peano Arithmetic
Sean Walsh
This paper presents new constructions of models of Hume's Principle and Basic Law V with restricted amounts of comprehension. The techniques used in these constructions are drawn f…
The Strength of Abstraction with Predicative Comprehension
Sean Walsh
Frege's theorem says that second-order Peano arithmetic is interpretable in Hume's Principle and full impredicative comprehension. Hume's Principle is one example of an abstraction…