Citations of:
On the weak Kleene scheme in Kripke's theory of truth
Journal of Symbolic Logic 56 (4):14521468 (1991)
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This book is a contribution to the flourishing field of formal and philosophical work on truth and the semantic paradoxes. Our aim is to present several theories of truth, to investigate some of their modeltheoretic, recursiontheoretic and prooftheoretic aspects, and to evaluate their philosophical significance. In Part I we first outline some motivations for studying formal theories of truth, fix some terminology, provide some background on Tarski’s and Kripke’s theories of truth, and then discuss the prospects of classical typefree truth. (...) 

The paper contains a survey on the complexity of various truth hierarchies arising in Kripke’s theory. I present some new arguments, and use them to obtain a number of interesting generalisations of known results. These arguments are both relatively simple, involving only the basic machinery of constructive ordinals, and very general. 

In this paper we study several translations that map models and formulae of the language of secondorder arithmetic to models and formulae of the language of truth. These translations are useful because they allow us to exploit results from the extensive literature on arithmetic to study the notion of truth. Our purpose is to present these connections in a systematic way, generalize some wellknown results in this area, and to provide a number of new results. Sections 3 and 4 contain (...) 