Advertisement

On Representing Semantics in Finite Models

  • Marcin Mostowski
Chapter
Part of the Synthese Library book series (SYLI, volume 320)

Abstract

This paper is continuation of research presented in (Mostowski, 2001). It gives some new results related to finite order hierarchy in finite models. They are obtained by the method of truth-definitions in finite models. Additionally we give an application od FM-representability theorem for studying densities of spectra. We finish with philosophical discussion of some problems raised by the reported research.

Keywords

Order Variable Order Logic Finite Model Combinatorial Object Peano Arithmetic 
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. Feferman, S. (1977). Theories of finite type related to mathematical practice. In Barwise, J., editor, Handbook of Mathematical Logic, pp. 913–971. North-Holland Publishing Company, Amsterdam.CrossRefGoogle Scholar
  2. Krynicki, M. and Mostowski, M. (1992). Decidability problems in language with Henkin quantifiers. Annals of Pure and Applied Logic, 58: 149–172.CrossRefGoogle Scholar
  3. Leivant, D. (1994). Higher order logic. In Gabbay, D. M., Hogger, C. J. and Robinson, J. A., editors, Handbook of Logic in Artificial Intelligence and Logic Programming, pp. 228–321. Clarendon Press, Oxford.Google Scholar
  4. Mostowski, M. (1993). Truth-Definitions in Finite Models. In manuscript. Mostowski, M. (1993b). The logic of divisibility. The Journal of Symbolic Logic,forthcoming.Google Scholar
  5. Mostowski, M. (2001). On representing concepts in finite models. Mathematical Logic Quaterly, Type=“Bold”>47: 523–533.Google Scholar
  6. Mostowski, M. (2003). Co w wiatach skonczonych moina powiedziec o semantyce. In preparation. (What we can say in finite worlds about semantics).Google Scholar
  7. Shoenfield, J. R,. (1993). Recursion Theory, Type=“Italic”>Lectures Notes in Logic. Springer-Verlag, Berlin-Heidelberg.Google Scholar
  8. Tarski, A. (1933). Pojecie prawdy w jezykach nauk dedukcyjnych. Nakladem Towarzystwa Naukowego Warszawskiego, Warszawa. (The concept of truth in formalized languages, translated from German by J. H. Woodger. In Tarski, A. (1956). Logic, Type=“Italic”>Semantics, Type=“Italic”>Metamathematics, pp. 152–278. The Clarendon Press, Oxford. )Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • Marcin Mostowski
    • 1
  1. 1.Warsaw UniversityPoland

Personalised recommendations