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Abstract model-theory and nets of C*-algebras: Noncommutative interpolation and preservation properties

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Models and Sets

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References

  1. Bratteli O., Robinson D.W., Operator Algebras and Quantum Statistical Mechanics, I,II, Springer, Berlin, 1979.

    Book  MATH  Google Scholar 

  2. Chang C.C., Keisler H.J., Model Theory, North-Holland, Amsterdam, second edition 1977.

    MATH  Google Scholar 

  3. Craig W., Three uses of the Herbrand-Gentzen theorem in relating model-theory and proof-theory, J.Symb.Logic,22 (1957) 269–285.

    Article  MathSciNet  MATH  Google Scholar 

  4. Driessler W., Comments on lightlike translations and applications in relativistic quantum field theory, Commun.Math.Phys.,44 (1975) 133–141.

    Article  MathSciNet  MATH  Google Scholar 

  5. Ebbinghaus H.D., Chapter II, in: Model-Theoretic Logics, J. Barwise, S. Feferman, Editors, Perspectives in Mathematical Logic, Springer, Berlin 1984, to appear.

    Google Scholar 

  6. Engelking R., General Topology, Monografie Matematyczne, Tom 60, PWN-Polish Scientific Publishers, Warszawa 1977.

    Google Scholar 

  7. Feferman S., Vaught R.L., The first-order properties of algebraic systems, Fund.Math., 47 (1959) 57–103.

    MathSciNet  MATH  Google Scholar 

  8. Flum J., Ziegler M., Topological Model Theory, Lecture Notes in Mathematics, Springer, Berlin 1980.

    Book  MATH  Google Scholar 

  9. Haag R., Kastler D., An algebraic approach to quantum field theory, J.Math.Phys., 5.7 (1964) 848–861.

    Article  MathSciNet  MATH  Google Scholar 

  10. Haag R., Kadison R.V., Kastler D., Nets of C*-algebras and classification of states, Commun.Math.Phys.,16 (1970) 81–104.

    Article  MathSciNet  MATH  Google Scholar 

  11. Mundici D., Compactness, interpolation and Friedman's third problem, Annals Math.Logic, 22 (1982) 197–211.

    Article  MathSciNet  MATH  Google Scholar 

  12. Mundici D., Duality between logics and equivalence relations, Transactions A.M.S., 270 (1982) 111–129.

    Article  MathSciNet  MATH  Google Scholar 

  13. Roos H., Independence of local algebras in quantum field theory, Commun.Math.Phys., 16(1970) 238–246.

    Article  MathSciNet  MATH  Google Scholar 

  14. Sakai S., C*-algebras and W*-algebras, Springer, Berlin 1971.

    Book  MATH  Google Scholar 

  15. Schlieder S., Einige Bemerkungen über Projektionsoperatoren, Commun.Math.Phys., 13 (1969) 216–225.

    Article  MathSciNet  MATH  Google Scholar 

  16. Shelah S., Generalized quantifiers and compact logics, Transactions A.M.S., 204 (1975) 342–364.

    Article  MATH  Google Scholar 

  17. Takesaki M., Theory of Operator Algebras I, Springer, Berlin 1979.

    Book  MATH  Google Scholar 

  18. Turumaru T., On the direct product of operator algebras IV, Tôhoku Math.J., 8 (1956) 281–285.

    Article  MathSciNet  MATH  Google Scholar 

  19. Batty C.J.K., Unbounded derivations of commutative C*-algebras, Commun.Math.Phys., 61 (1978) 261–266.

    Article  MathSciNet  MATH  Google Scholar 

  20. Bratteli O., Inductive limits of finite dimensional C*-algebras, Transactions A.M.S., 171 (1972) 195–234.

    MathSciNet  MATH  Google Scholar 

  21. Bratteli O., Structure spaces of approximately finite dimensional C*-algebras, Journal of Funct.Anal., 16 (1974) 192–204.

    Article  MathSciNet  MATH  Google Scholar 

  22. Bratteli O., The center of approximately finite-dimensional C*-algebras, Journal of Funct.Anal., 21 (1976) 195–202.

    Article  MathSciNet  MATH  Google Scholar 

  23. Bratteli O., Elliott G.A., Structure spaces of approximately finite dimensional C*-algebras, II, Journal of Funct.Anal., 30 (1978) 74–82.

    Article  MathSciNet  MATH  Google Scholar 

  24. Choi M.D., Lifting projections from quotient C*-algebras, Journal of Operator Theory, 10 (1983) 21–30.

    MathSciNet  MATH  Google Scholar 

  25. Effros E.G., On the structure theory of C*-algebras: some old and new problems. Proceedings of Symp.in Pure Math., A.M.S., vol.38 (1982) part 1, 19–35.

    Article  MathSciNet  Google Scholar 

  26. Goodman F.M., Closed derivations in commutative C*-algebras, Journal of Funct.Anal., 39 (1980) 308–346.

    Article  MathSciNet  MATH  Google Scholar 

  27. Hofmann K.H., Thayer F.X., Approximately finite-dimensional C*-algebras, Dissertationes Mathematicae (Rozprawy Mat.), 174 (1980) 64 pp.

    Google Scholar 

  28. Lazar A.J., AF algebras with a lattice of projections, Math.Scand., 50 (1982) 135–144.

    MathSciNet  MATH  Google Scholar 

  29. Lazar A.J., AF algebras with directed sets of finite dimensional *-subalgebras, Transactions A.M.S., 275 (1983) 709–721.

    MathSciNet  MATH  Google Scholar 

  30. Lazar A.J., Taylor D.C., Approximately finite dimensional C*-algebras and Bratteli diagrams, Transactions A.M.S.259 (1980) 599–619.

    MathSciNet  MATH  Google Scholar 

  31. Pedersen G.K., C*-algebras and their Automorphism Groups, Academic Press, London (1979).

    MATH  Google Scholar 

  32. Thayer F.X., The Weyl-von Neumann theorem for approximately finite C*-algebras, Indiana Math.J., 24(1975) 875–877.

    Article  MathSciNet  MATH  Google Scholar 

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Gert H. Müller Michael M. Richter

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© 1984 Springer-Verlag

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Mundici, D. (1984). Abstract model-theory and nets of C*-algebras: Noncommutative interpolation and preservation properties. In: Müller, G.H., Richter, M.M. (eds) Models and Sets. Lecture Notes in Mathematics, vol 1103. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099394

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  • DOI: https://doi.org/10.1007/BFb0099394

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  • Online ISBN: 978-3-540-39115-9

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