Skip to main content

Set theory in infinitary languages

Part of the Lecture Notes in Mathematics book series (LNM,volume 499)

This is a preview of subscription content, access via your institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • BARWISE, J. 1968a Implicit definability and compactness in infinitary languages, in: The syntax and semantics of infinitary languages (ed. by J. Barwise), 1–35. Lecture Notes in Mathematics, Vol. 72, Springer-Verlag, Berlin-Heidelberg-New York (1968)

    Google Scholar 

  • -1969a Infinitary logic and admissible sets, Journ. Symb. Logic 34 (1969), 226–252

    CrossRef  MATH  MathSciNet  Google Scholar 

  • -1969b Applications of strict ∏ 11 predicates to infinitary logic, Journ. Symb. Logic 34 (1969), 409–423

    CrossRef  MATH  MathSciNet  Google Scholar 

  • BARWISE, J., GANDY, R.O. and MOSCHOWAKIS, Y.N. 1971 The next admissible set, Journ. Symb. Logic 36 (1971), 108–120

    CrossRef  MATH  Google Scholar 

  • BOWEN, K.A. 1973 Infinite forcing and natural models of set theory, Bull. Acad. Polon. Sci. XXI, 3 (1973), 195–199.

    MathSciNet  Google Scholar 

  • CHANG, C.C. 1971 Sets constructible using Lkk, in: SCOTT 1971, 1–8

    Google Scholar 

  • FELGNER, U. 1971 Models of ZF-set theory, Lecture Notes in Mathematics, Vol. 223, Springer-Verlag, Berlin-Heidelberg-New York (1971), VI + 173 pp.

    MATH  Google Scholar 

  • GLOEDE, K. 1971 Filters closed under Mahlo's and Gaifman's operation, in: Proc. Cambridge Summer School in Mathematical Logic (ed. by A.R.D. Mathias and H. Rogers), 495–530. Lecture Notes in Maths, Vol. 337. Springer-Verlag, Berlin-Heidelberg-New York

    Google Scholar 

  • GLOEDE, K. 1974 Mengenlehre in infinitären Sprachen, Universität Heidelberg (1974), 188 pp.

    Google Scholar 

  • GÖDEL, K. 1940 The consistency of the axiom of choice and the generalized continuum hypothesis, Annals of Math. Studies 3, Princeton, N. J. (2nd printing 1951, 74 pp.)

    Google Scholar 

  • JENSEN, R. B. and KARP, C. 1971 Primitive recursive set functions in: SCOTT 1971, 143–167

    Google Scholar 

  • KARP, C. 1964. Languages with expressions of infinite length, North-Holland Publ. Co., Amsterdam (1964), IX + 183 pp.

    MATH  Google Scholar 

  • KEISLER, J.H. 1971 Model theory for infinitary logic, North-Holland Publ. Co., Amsterdam (1971), X + 208 pp.

    MATH  Google Scholar 

  • LEVY, A. 1960 Axiom schemata of strong infinity in axiomatic set theory, Pacific J. Math. 10 (1960), 223–238

    MATH  MathSciNet  Google Scholar 

  • LEVY, A. 1965 A hierarchy of formulas in set theory, Memoirs Am. Math. Soc. 57, Providence, R.I., 76 pp.

    Google Scholar 

  • MOSTOWSKI, A. 1949 An undecidable arithmetical statement, Fund. Math. 36 (1949), 143–164

    MATH  MathSciNet  Google Scholar 

  • REINHARDT, W.N. 1970 Ackermann's set theory equals ZF, Annals of Math. Logic 2 (1970), 189–249

    CrossRef  MATH  MathSciNet  Google Scholar 

  • SCOTT, D. 1971 (editor) Axiomatic set theory. Proc. of Symposia in Pure Mathematics 13, Providence, R.I.

    Google Scholar 

  • SCOTT, D. and MYHILL, J. 1971 Ordinal definability, in SCOTT 1971, 271–278

    Google Scholar 

  • TARSKI, A., MOSTOWKI, A. and ROBINSON, R.M. 1953 Undecidable theories. North-Holland Publ. Co., Amsterdam (1953), 98 pp.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1975 Springer-Verlag

About this paper

Cite this paper

Gloede, K. (1975). Set theory in infinitary languages. In: Müller, G.H., Oberschelp, A., Potthoff, K. (eds) ⊨ISILC Logic Conference. Lecture Notes in Mathematics, vol 499. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0079424

Download citation

  • DOI: https://doi.org/10.1007/BFb0079424

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07534-9

  • Online ISBN: 978-3-540-38022-1

  • eBook Packages: Springer Book Archive