Abstract

this article will deal only with the intensional approach. The reader who wants to see the numeralwise representability approach can consult Smorynski [1977] and any number of textbooks such as Mendelson [1987]. The intensional approach is due to Feferman [1960]. An e#ective unification of the two approaches can be given using the fact (independently due to Wilkie and to Nelson [1986]) that I# 0 +# 1 and S 2 are interpretable in Q ; since both I# 0 +# 1 and S 2 admit a relatively straightforward intensional arithmetization of metamathematics (see Wilkie and Paris [1987] and Buss [1986]), this allows strong forms of incompleteness obtained via the intensional approach to apply also to the theory Q ; paragraph 2.1.4 below sketches how the interpretation of S 2 in Q can be used to give an intensional arithmetization in Q . The book of Smullyan [1992] gives a modern, in-depth treatment of Godel's incompleteness theorems

Citations

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