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Quantifiers and Logical Reductions

  • Heinz-Dieter Ebbinghaus
  • Jörg Flum
Part of the Perspectives in Mathematical Logic book series (PML)

Abstract

In Chapter 6 we have seen that least fixed-point logic FO(LFP) captures PTIME, but does not strongly capture PTIME. In fact, it is open until now, whether there is any “natural” logic strongly capturing PTIME. At a first glance the following idea might be successful: Consider, for example, FO(LFP). One could think of strengthening it by adding some PTIME concepts, thereby enlarging its expressive power just up to PTIME. In traditional model theory there is a well-established method to enrich logics by new concepts, namely by adjoining so-called Lindström quantifiers. We have already met such quantifiers, for example, the counting quantifiers (cf. section 2.4).

Keywords

Equality Type Turing Machine Logical Reduction Relation Symbol Input Tape 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Heinz-Dieter Ebbinghaus
    • 1
  • Jörg Flum
    • 1
  1. 1.Institute of Mathematical LogicUniversity of FreiburgFreiburgGermany

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