Advertisement

Arithmetic Complexity of the Predicate Logics of Complete Arithmetic Theories

  • Valeri Plisko
Chapter
Part of the Synthese Library book series (SYLI, volume 320)

Abstract

It seems that the most natural problem in mathematical logic is studying the logics of mathematical theories. If the logics of first-order theories are considered, the situation can be formalized in the following way. Let T be a first-order theory, i.e. a set of closed formulas in a first-order language L. A closed predicate formula is called T-valid if each its closed L-instance is in T. We denote the set of T-valid predicate formulas by L(T) and call it the predicate logic of the theory T.

Keywords

Atomic Formula Predicate Logic Closed Formula Arithmetic Complexity Arithmetic Theory 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Kleene, S. C. (1952). Introduction to Metamathematics. Van Nostrand, New York.Google Scholar
  2. Plisko, V. E. (1978). Nekotorye varianty poniatia realizuemosti dlia predikatnyh formul. Izvestia Akademii Nauk SSSR. Seria matematicheskaia, 42:636–653. (Some variants of the notion of realizability for predicate formulas. Izvestia Akademii Nauk SSSR. Seria matematicheskaia.42:636–653.) Google Scholar
  3. Plisko, V. E. (1990). Konstruktivnaia formalizatsia teoremy Tennenbauma i ee primemenenia. Matematicheskie Zametki, 48: 108–118. (Constructive formalization of Tennenbaum’s theorem and its applications. Mat. Zametki, 48:108–118.)Google Scholar
  4. Plisko, V. E. (1992). Ob arifmeticheskoi slozhnosti nekotoryh konstruktivnyh logik. Matematicheskie Zametki, 52: 94–104. (On arithmetic complexity of certain constructive logics. Matematicheskie Zametki, 52:94–104.)Google Scholar
  5. Rogers, H. (1967). Theory of Recursive Functions and Effective Computability. MIT Press, Cambridge, Mass.Google Scholar
  6. Tennenbaum, S. (1959). Non-Archimedean systems of arithmetic. Notices of the American Mathematical Society, 6: 270–283.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • Valeri Plisko
    • 1
  1. 1.Moscow State UniversityRussia

Personalised recommendations