Bibliography on Realizability

AbstractThis document is a bibliography on realizability and related matters. It has been collected by Lars Birkedal based on submissions from the participants in “A Workshop on Realizability Semantics and Its Applications”, Trento, Italy, June 30–July 1, 1999. It is available in BibTEX format at the following URL: http://www.cs.cmu.edu./~birkedal/realizability-bib.html

Hyperintensional Ω-Logic

This essay examines the philosophical significance of the consequence relation defined in the $\Omega$-logic for set-theoretic languages. I argue that, as with second-order logic, the hyperintensional profile of validity in $\Omega$-Logic enables the property to be epistemically tractable. Because of the duality between coalgebras and algebras, Boolean-valued models of set theory can be interpreted as coalgebras. In Section \textbf{2}, I demonstrate how the hyperintensional profile of $\Omega$-logical validity can be countenanced within a coalgebraic logic. Finally, in Section \textbf{3}, the philosophical significance of the characterization of the hyperintensional profile of $\Omega$-logical validity for the philosophy of mathematics is examined. I argue (i) that $\Omega$-logical validity is genuinely logical, and (ii) that it provides a hyperintensional account of formal grasp of the concept of `set'. Section \textbf{4} provides concluding remarks