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Interpretability Logic

In: Mathematical Logic

Author

Listed:
  • Albert Visser

    (University of Utrecht, Department of Philosophy)

Abstract

Interpretations are much used in metamathematics. The first application that comes to mind is their use in reductive Hilbert-style programs Think of the kind of program proposed by Simpson, Feferman or Nelson (see Simpson[1988], Feferman[1988], Nelson[1986]). Here they serve to compare the strength of theories, or better to prove conservation results within a properly weak theory. An advantage of using interpretations is that even if their use should — perhaps- be classified as a proof-theoretical method, it is often possible to employ a model-theoretical heuristics. An example is given in section 7.2 where a conservation result due to Paris & Wilkie, which is proven by a model-theoretical argument, is formalized in a weak theory. For more discussion of and perspective on the use of interpretability in reductive programs the reader is referred to Feferman[1988].

Suggested Citation

  • Albert Visser, 1990. "Interpretability Logic," Springer Books, in: Petio Petrov Petkov (ed.), Mathematical Logic, pages 175-209, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4613-0609-2_13
    DOI: 10.1007/978-1-4613-0609-2_13
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