The Cantor's attic library

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Step up the ladder towards wisdom, photo by Sigfrid Lundberg

Welcome to the library, our central repository for references cited here on Cantor's attic.

Library holdings

  1. Abramson, Fred and Harrington, Leo and Kleinberg, Eugene and Zwicker, William. Flipping properties: a unifying thread in the theory of large cardinals. Ann Math Logic 12(1):25--58, 1977. MR   bibtex
  2. Bagaria, Joan and Casacuberta, Carles and Mathias, A R D and Rosicky, Jirí. Definable orthogonality classes in accessible categories are small. Unpublished (submitted for publication) www   bibtex
  3. Bagaria, Joan and Hamkins, Joel David and Tsaprounis, Konstantinos and Usuba, Toshimichi. Superstrong and other large cardinals are never {Laver} indestructible. www   arχiv   bibtex
  4. Baumgartner, James. Ineffability properties of cardinals. I. Infinite and finite sets (Colloq., Keszthely, 1973; dedicated to P. Erdős on his 60th birthday), Vol. I, pp. 109--130. Colloq. Math. Soc. János Bolyai, Vol. 10, Amsterdam, 1975. MR   bibtex
  5. Blass, Andreas. Chapter 6: Cardinal characteristics of the continuum. Handbook of Set Theory , 2010. www   bibtex
  6. Cantor, Georg. Contributions to the Founding of the Theory of Transfinite Numbers. Dover, New York, 1955. (Original year was 1915) www   bibtex
  7. Cody, Brent and Gitman, Victoria. Easton's theorem for Ramsey and strongly Ramsey cardinals. (In preparation) bibtex
  8. Corazza, Paul. The Wholeness Axiom and Laver sequences. Annals of Pure and Applied Logic pp. 157--260, October, 2000. bibtex
  9. Corazza, Paul. The gap between ${\rm I}_3$ and the wholeness axiom. Fund Math 179(1):43--60, 2003. www   DOI   MR   bibtex
  10. Dodd, Anthony and Jensen, Ronald. The core model. Ann Math Logic 20(1):43--75, 1981. www   DOI   MR   bibtex
  11. Erdős, Paul and Hajnal, Andras. Some remarks concerning our paper ``On the structure of set-mappings''. Non-existence of a two-valued $\sigma $-measure for the first uncountable inaccessible cardinal. Acta Math Acad Sci Hungar 13:223--226, 1962. MR   bibtex
  12. Erdős, Paul and Hajnal, Andras. On the structure of set-mappings. Acta Math Acad Sci Hungar 9:111--131, 1958. MR   bibtex
  13. Evans, C D A and Hamkins, Joel David. Transfinite game values in infinite chess. (under review) www   arχiv   bibtex
  14. Foreman, Matthew and Kanamori, Akihiro. Handbook of Set Theory. First, Springer, 2010. (This book is actually a compendium of articles from multiple authors) www   bibtex
  15. Gaifman, Haim. Elementary embeddings of models of set-theory and certain subtheories. Axiomatic set theory (Proc. Sympos. Pure Math., Vol. XIII, Part II, Univ. California, Los Angeles, Calif., 1967), pp. 33--101, Providence R.I., 1974. MR   bibtex
  16. Gitman, Victoria. Ramsey-like cardinals. The Journal of Symbolic Logic 76(2):519-540, 2011. www   arχiv   MR   bibtex
  17. Gitman, Victoria and Welch, Philip. Ramsey-like cardinals II. J Symbolic Logic 76(2):541--560, 2011. www   arχiv   MR   bibtex
  18. Gitman, Victoria and Johnstone, Thomas. Indestructibility for Ramsey and Ramsey-like cardinals. (In preparation) bibtex
  19. Goldblatt, Robert. Lectures on the Hyperreals. Springer, 1998. bibtex
  20. Goldstern, Martin and Shelah, Saharon. The Bounded Proper Forcing Axiom. J Symbolic Logic 60(1):58--73, 1995. www   bibtex
  21. Hamkins, Joel David and Lewis, Andy. Infinite time Turing machines. J Symbolic Logic 65(2):567--604, 2000. www   arχiv   DOI   MR   bibtex
  22. Hamkins, Joel David. Infinite time Turing machines. Minds and Machines 12(4):521--539, 2002. (special issue devoted to hypercomputation) www   arχiv   bibtex
  23. Hamkins, Joel David. Supertask computation. Classical and new paradigms of computation and their complexity hierarchies23:141--158, Dordrecht, 2004. (Papers of the conference ``Foundations of the Formal Sciences III'' held in Vienna, September 21-24, 2001) www   arχiv   DOI   MR   bibtex
  24. Hamkins, Joel David. The wholeness axioms and V=HOD. Arch Math Logic 40(1):1--8, 2001. www   arχiv   DOI   MR   bibtex
  25. Hamkins, Joel David. Tall cardinals. MLQ Math Log Q 55(1):68--86, 2009. www   DOI   MR   bibtex
  26. Hamkins, Joel David and Kirmayer, Greg and Perlmutter, Norman. Generalizations of the {Kunen} inconsistency. Annals of Pure and Applied Logic 163(12):1872 - 1890, 2012. www   arχiv   DOI   bibtex
  27. Hamkins, Joel David and Johnstone, Thomas A. Resurrection axioms and uplifting cardinals. www   arχiv   bibtex
  28. Jech, Thomas J. Set Theory. Third, Springer-Verlag, Berlin, 2003. (The third millennium edition, revised and expanded) bibtex
  29. Jensen, Ronald and Kunen, Kenneth. Some combinatorial properties of $L$ and $V$. Unpublished, 1969. www   bibtex
  30. Kanamori, Akihiro and Magidor, Menachem. The evolution of large cardinal axioms in set theory. Higher set theory (Proc. Conf., Math. Forschungsinst., Oberwolfach, 1977)669:99--275, Berlin, 1978. www   MR   bibtex
  31. Kanamori, Akihiro. The higher infinite. Second, Springer-Verlag, Berlin, 2009. (Large cardinals in set theory from their beginnings, Paperback reprint of the 2003 edition) www   bibtex
  32. Kanamori, Akihiro and Reinhardt, William N and Solovay, Robert M. Strong axioms of infinity and elementary embeddings. , 1978. (In ''Annals of Mathematical Logic'', '''13'''(1978)) www   bibtex
  33. Kunen, Kenneth. Saturated Ideals. J Symbolic Logic 43(1):65--76, 1978. www   bibtex
  34. Laver, Richard. Implications between strong large cardinal axioms. Ann Math Logic 90(1--3):79--90, 1997. MR   bibtex
  35. Mitchell, William J. The Covering Lemma. Handbook of Set Theory , 2001. www   bibtex
  36. Miyamoto, Tadatoshi. A note on weak segments of PFA. Proceedings of the sixth Asian logic conference pp. 175--197, 1998. bibtex
  37. Sharpe, Ian and Welch, Philip. Greatly Erdős cardinals with some generalizations to the Chang and Ramsey properties. Ann Pure Appl Logic 162(11):863--902, 2011. www   DOI   MR   bibtex
  38. Schanker, Jason A. Partial near supercompactness. Ann Pure Appl Logic , 2012. (In Press.) www   DOI   bibtex
  39. Schanker, Jason A. Weakly measurable cardinals. MLQ Math Log Q 57(3):266--280, 2011. www   DOI   bibtex
  40. Schanker, Jason A. Weakly measurable cardinals and partial near supercompactness. Ph.D. Thesis, CUNY Graduate Center, 2011. bibtex
  41. Schindler, Ralf-Dieter. Proper forcing and remarkable cardinals. Bull Symbolic Logic 6(2):176--184, 2000. www   DOI   MR   bibtex
  42. Silver, Jack. A large cardinal in the constructible universe. Fund Math 69:93--100, 1970. MR   bibtex
  43. Silver, Jack. Some applications of model theory in set theory. Ann Math Logic 3(1):45--110, 1971. MR   bibtex
  44. Suzuki, Akira. Non-existence of generic elementary embeddings into the ground model. Tsukuba J Math 22(2):343--347, 1998. MR   bibtex | Abstract
  45. Suzuki, Akira. No elementary embedding from $V$ into $V$ is definable from parameters. J Symbolic Logic 64(4):1591--1594, 1999. www   DOI   MR   bibtex
  46. Viale, Matteo and Weiß, Christoph. On the consistency strength of the proper forcing axiom. Advances in Mathematics 228(5):2672--2687, 2011. arχiv   MR   bibtex
  47. Welch, Philip. The Lengths of Infinite Time Turing Machine Computations. Bulletin of the London Mathematical Society 32(2):129--136, 2000. bibtex
  48. Welch, Philip. Eventually Infinite Time Turing Machine Degrees: Infinite Time Decidable reals. Journal of Symbolic Logic 65(3):1193--1203, 2000. bibtex
  49. Zapletal, Jindrich. A new proof of Kunen's inconsistency. Proc Amer Math Soc 124(7):2203--2204, 1996. www   MR   bibtex

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