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Hilbert’s choice operators τ and ε, when added to intuitionistic logic, strengthen it. In the presence of certain extensionality axioms they produce classical logic, while in the presence of weaker decidability conditions for terms they produce various superintuitionistic intermediate logics. In this thesis, I argue that there are important philosophical lessons to be learned from these results. To make the case, I begin with a historical discussion situating the development of Hilbert’s operators in relation to his evolving program in the (...) 

I argue that we can and should extend Tarski's modeltheoretic criterion of logicality to cover indefinite expressions like Hilbert's ɛ operator, Russell's indefinite description operator η, and abstraction operators like 'the number of'. I draw on this extension to discuss the logical status of both abstraction operators and abstraction principles. 

This is the ASL report on the 7th Latin American Symposium on Mathematical Logic held in Campinas, SP, Brazil, from July 29 August 02, 1985. 

This paper focuses on two notions of effectiveness which are not treated in detail elsewhere. Unlike the standard computability notion, which is a property of functions themselves, both notions of effectiveness are properties of interpreted linguistic presentations of functions. It is shown that effectiveness is epistemically at least as basic as computability in the sense that decisions about computability normally involve judgments concerning effectiveness. There are many occurrences of the present notions in the writings of logicians; moreover, consideration of these (...) 

The general theory of variable binding term operators is an interesting recent development in logic. It opens up a rich class of semantic and modeltheoretic problems. In this paper we survey the recent literature on the topic, and offer some remarks on its significances and on its connections with other branches of mathematical logic. 