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Interpolation, preservation, and pebble games

Published online by Cambridge University Press:  12 March 2014

Jon Barwise  and
Johan van Benthem
Jon Barwise
Affiliation:
Departments of Computer Science, Mathematics and Philosophy, Indiana University, Bloom Ington, IN 47405, USA E-mail: [email protected]
Johan van Benthem
Affiliation:
Institute for Logic, Language and Computation, University of Amsterdam, Amsterdam, The Netherlands E-mail: [email protected]
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Abstract

Preservation and interpolation results are obtained for L∞ω and sublogics ⊆ L∞ω such that equivalence in can be characterized by suitable back-and-forth conditions on sets of partial isomorphisms.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 2 , June 1999 , pp. 881 - 903
Copyright
Copyright © Association for Symbolic Logic 1999

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References

REFERENCES

[1] Andréka, H., van Benthem, J., and Németi, I., Modal logics and bounded fragments of predicate logic, Journal of Philosophical Logic, vol. 27 (1998), pp. 217–274.CrossRefGoogle Scholar
[2] Baltag, A., Interpolation and preservation for pebble logics, this Journal, vol. 64 (1999), pp. 846–858 (this issue).Google Scholar
[3] Barwise, J., Back and forth through infinitary logic, Studies in model theory, (Morley, M., editor), MAA Studies in Mathematics, 1973, pp. 5–35.Google Scholar
[4] Barwise, J., Axioms for abstract model theory, Annals of Math Logic, vol. 7 (1974), pp. 221–265.Google Scholar
[5] Barwise, J., Admissible sets and structures, Springer-Verlag, 1975.Google Scholar
[6] Barwise, J., On Moschovakis closure ordinals, this Journal, vol. 42 (1977), pp. 292–298.Google Scholar
[7] Barwise, J. and Kunen, K., Hanf numbers for fragments of L∈ω , Israel Journal of Mathematics, vol. 10 (1971), pp. 306–320.CrossRefGoogle Scholar
[8] Barwise, J. and Moschovakis, Y., Global inductive definability, this Journal, vol. 43 (1978), pp. 521–534.Google Scholar
[9] Barwise, J. and Moss, L., Vicious Circles, CSLI Publications, Stanford, 1996.Google Scholar
[10] Chang, C.C., Some remarks on the model theory of infinitary languages, The syntax and semantics of infinitary languages (Barwise, J., Editor), LNM 72, Springer-Verlag, 1968.Google Scholar
[11] d. Agostino, G., van Benthem, J., Montanari, A., and Policriti, A., Modal deduction in second-order logic and set theory, Journal of Logic and Computation, vol. 7 (1997), pp. 251£265.Google Scholar
[12] Dawar, A., Feasible computation through model theory, Ph.D. dissertation , University of Pennsylvania, 1993.Google Scholar
[13] Ebbinghaus, H-D and Flum, J., Finite model theory, Springer-Verlag, 1995.Google Scholar
[14] Karp, C., Finite quantifier equivalence, The theory of models (Addison, J. et al., editors), N. Holland, 1965, PP. 407–412.Google Scholar
[15] Keisler, H. J., Model theory for infinitary logic, N. Holland, 1971.Google Scholar
[16] Lopez-Escobar, E., An interpolation theorem for denumerabfy long sentences, Fundamenta Mathematicae, vol. LVII (1965), pp. 253–272.Google Scholar
[17] Lopez-Escobar, E., On definable well-orderings, Fundamenta Mathematicae, vol. LVIX (1966), pp. 13–21, 299–300.Google Scholar
[18] Malitz, J., Infinitary analogues of theorems from first-order model theory, this Journal, vol. 36 (1971), pp. 216–228.Google Scholar
[19] Morley, M., Omitting classes of elements, The theory of models (Addison, J. et al., editors), N. Holland, 1965, PP. 265–273.Google Scholar
[20] Sacks, G., Saturated model theory, Benjamin, 1972.Google Scholar
[21] Sain, I., Beth's and Craig's properties via epimorphism and amalgamation in algebraic logic, Algebraic logic and universal algebra in computer science (Bergman, C. et al., editors), LNCS, Springer-Verlag, 1990, pp. 209–226.Google Scholar
[22] Scott, D., Invariant borel sets, Fundamenta Mathematicae, vol. 56 (1964), pp. 117–128.Google Scholar
[23] van Benthem, J., Exploring logical dynamics, Studies in Logic, Language and Information, CSLI Publications, Stanford.Google Scholar
[24] van Benthem, J., Modal correspondence theory, Ph.D. thesis , Mathematics Institute, University of Amsterdam, 1976.Google Scholar
[25] van Benthem, J., Modal logic and classical logic, Bibliopolis, Naples, 1985.Google Scholar
[26] van Benthem, J., Language in Action, N. Holland, Amsterdam, 1991.Google Scholar
[27] van Benthem, J., Programming operations that are safe for bisimulation, Studia Logica, vol. 60 (1998), pp. 311–330.Google Scholar