Skip to main content

Filters closed under MAHLO's and GAIFMAN's operation

  • Set Theory And Combinatorics
  • Conference paper
  • First Online:
Cambridge Summer School in Mathematical Logic

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 337))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  • P. Bernays [1962] Zur Frage der Unendlichkeitsschemata in der axiomatischen Mengenlehre, Essays ded. to A.A. Fraenkel, pp.3–49, North-Holland Publ. Co. 1962

    Google Scholar 

  • G. Fodor [1956] Eine Bemerkung zur Theorie der regressiven Funktionen, Acta Sci. Math. (Szeged) 17 (1956), pp. 139–142

    MathSciNet  MATH  Google Scholar 

  • [1966] On stationary sets and regressive functions, ibid. 27 (1966), pp. 105–110

    MathSciNet  MATH  Google Scholar 

  • [1966] On a process concerning inaccessible cardinals I, ibid. 27 (1966), pp. 111–124

    MathSciNet  MATH  Google Scholar 

  • G. Fodor and A. Hajnal [1967] On regressive functions and α-complete ideals, Bull. Acad. Pol. Sci. 15 (1967), pp.427–432

    MathSciNet  MATH  Google Scholar 

  • G. Fodor and A. Máté [1969] Cardinals inaccessible with respect to a function defined on pairs of cardinals, Acta Sci. Math. (Szeged) 30 (1969), pp. 107–111

    MathSciNet  MATH  Google Scholar 

  • H. Gaifman [1967] A generalization of Mahlo's method for obtaining large cardinal numbers, Israel J. Math. 5 (1967), pp. 188–200

    Article  MathSciNet  MATH  Google Scholar 

  • K. Gödel [1940] The consistency of the axiom of choice and of the generalized continuum hypothesis with the axioms of set theory (Annals of Math. Studies No. 3), Princeton, New Jersey, 1940

    Google Scholar 

  • A. Hajnal [1969] Ulam matrices for inaccessible cardinals, Bull. Acad. Pol. Sci. 17 (1969), pp. 683–688

    MathSciNet  MATH  Google Scholar 

  • W. Hanf [1964] Incompactness in laguages with infinitely long expressions, Fund. Math. 53 (1964), pp. 309–324

    MathSciNet  MATH  Google Scholar 

  • W. Hanf and D. Scott [1961] Classifying inaccessible cardinals (abstract), Notices AMS 8 (1961), p.445

    Google Scholar 

  • R.B. Jensen [1967] Große Kardinalzahlen, Notes of lectures given at the Mathematisches Forschungsinstitut Oberwolfach (Germany), 1967

    Google Scholar 

  • [1969] Souslin's hypothesis = weak compactness in L (abstract), Notices AMS 16 (1969), p.842

    Google Scholar 

  • C. Karp [1964] Languages with expressions of infinite length, North-Holland Publ. Co. 1964, XIX+183 pp.

    Google Scholar 

  • H.J. Keisler [1962] Mahlo's operation and the existence of α-complete prime ideals (abstract), Notices AMS 9 (1962), p.339

    Google Scholar 

  • H.J. Keisler and A. Tarski [1964] From accessible to inaccessible cardinals, Fund. Math. 53 (1964), pp. 225–308, Corrections ibid. 57 (1965), p.119

    MathSciNet  MATH  Google Scholar 

  • H.J. Keisler and F. Rowbottom [1965] Constructible sets and weakly compact cardinals (abstract), Notices AMS 12 (1965), pp. 373–374

    Google Scholar 

  • K. Kunen [1970] Some applications of iterated ultrapowers in set theory, Annals of Math. Logic 1 (1970), pp. 179–227

    Article  MathSciNet  MATH  Google Scholar 

  • A. Levy [1960] On the principles of reflection in axiomatic set theory, Pacific J. Math. 10 (1960), pp.223–238

    Article  MathSciNet  MATH  Google Scholar 

  • A. Levy [1965] A hierarchy of formulas in set theory, Memoirs of the AMS No. 57, Providence, Rhode Island, 1965

    Google Scholar 

  • [1967] The sizes of the indescribable cardinals, Proc. U.C.L.A. Summer Institute on Set Theory 1967, to appear

    Google Scholar 

  • P. Mahlo [1911–1913] Ãœber lineare transfinite Mengen; Zur Theorie und Anwendung der -Zahlen, Berichte über die Verhandlungen der Königl. Sächs. Gesellschaft der Wissenschaften zu Leipzig, Math.-Phys. Klasse 63 (1911), pp. 187–225; ibid. 64 (1912), pp. 108–112; ibid. 65 (1913), pp. 268–282

    Google Scholar 

  • A. Máté [1971] Incompactness in infinitary languages with respect to Boolean-valued interpretations, University of Szeged (1971), 55 pp. (mimeographed)

    Google Scholar 

  • A.R.D. Mathias [1968] A survey of recent results in set theory, Proc. U.C.L.A. Summer Institute on Set Theory 1967, to appear

    Google Scholar 

  • R. Montague and R. Vaught [1959] Natural models of set theory, Fund. Math. 47 (1959), pp. 219–242

    MathSciNet  MATH  Google Scholar 

  • D. Scott and R.M. Solovay [1967] Boolean-valued models for set theory, Proc. U.C.L.A. Summer Institute on Set Theory 1967, to appear

    Google Scholar 

  • J.C. Shepherdson [1951–1953] Inner models for set theory, Journ. Symb. Logic 16 (1951), pp. 161–190; ibid. 17 (1952), pp. 225–237; ibid. 18 (1953), pp. 145–167

    Article  MathSciNet  MATH  Google Scholar 

  • J. Silver [1966] Some applications of model theory in set theory, Thesis, Univ. of California, Berkeley, 1966, 110 pp.

    Google Scholar 

  • R.M. Solovay [1967a] Real-valued measurable cardinals, Proc. U.C.L.A. Summer Institute on Set Theory 1967, to appear

    Google Scholar 

  • [1967b] Solution of a problem of Fodor and Hajnal, ibid.

    Google Scholar 

  • [1967c] If ZF+MC+AC is consistent, then ZF+AC+2 Ï° 0 is r.v.m. is consistent, ibid.

    Google Scholar 

  • G. Takeuti [1961] Axioms of infinity of set theory, Journ. Math. Soc. Japan 13 (1961), pp. 220–233

    Article  MathSciNet  MATH  Google Scholar 

  • G. Takeuti [1969] The universe of set theory, in: Foundations of Mathematics, Symposium papers comm. the 60th birthday of K. Gödel, pp. 74–128, Springer-Verlag, 1969

    Google Scholar 

  • R. Vaught [1963] Indescribable cardinals (abstract), Notices AMS 10 (1963), p. 126

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

A. R. D. Mathias H. Rogers

Rights and permissions

Reprints and permissions

Copyright information

© 1973 Springer-Verlag

About this paper

Cite this paper

Gloede, K. (1973). Filters closed under MAHLO's and GAIFMAN's operation. In: Mathias, A.R.D., Rogers, H. (eds) Cambridge Summer School in Mathematical Logic. Lecture Notes in Mathematics, vol 337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066787

Download citation

  • DOI: https://doi.org/10.1007/BFb0066787

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05569-3

  • Online ISBN: 978-3-540-36884-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics