The Cantor's attic library

From Cantor's Attic
Jump to: navigation, search
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 Unpublished (submitted for publication) www   bibtex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. Boney, Will. Model Theoretic Characterizations of Large Cardinals. www   bibtex
  7. Cantor, Georg. Contributions to the Founding of the Theory of Transfinite Numbers. Dover, New York, 1955. (Original year was 1915) www   bibtex
  8. Cody, Brent, Gitik, Moti, Hamkins, Joel David, and Schanker, Jason. The Least Weakly Compact Cardinal Can Be Unfoldable, Weakly Measurable and Nearly θ-Supercompact. , 2013. www   bibtex
  9. Cody, Brent and Gitman, Victoria. Easton's theorem for Ramsey and strongly Ramsey cardinals. (In preparation) bibtex
  10. Corazza, Paul. The Wholeness Axiom and Laver sequences. Annals of Pure and Applied Logic pp. 157--260, October, 2000. bibtex
  11. Corazza, Paul. The gap between ${\rm I}_3$ and the wholeness axiom. Fund Math 179(1):43--60, 2003. www   DOI   MR   bibtex
  12. Dodd, Anthony and Jensen, Ronald. The core model. Ann Math Logic 20(1):43--75, 1981. www   DOI   MR   bibtex
  13. 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
  14. Erdős, Paul and Hajnal, Andras. On the structure of set-mappings. Acta Math Acad Sci Hungar 9:111--131, 1958. MR   bibtex
  15. Eskrew, Monroe and Hayut, Yair. On the consistency of local and global versions of Chang's Conjecture. , 2016. www   arχiv   bibtex
  16. Esser, Olivier. Inconsistency of GPK+AFA. Mathematical Logic Quarterly 42:104--108, 1996. www   DOI   bibtex
  17. Esser, Olivier. An Interpretation of the Zermelo-Fraenkel Set Theory and the Kelley-Morse Set Theory in a Positive Theory. Mathematical Logic Quarterly 43:369--377, 1997. www   DOI   bibtex
  18. Esser, Olivier. On the Consistency of a Positive Theory. Mathematical Logic Quarterly 45:105--116, 1999. www   DOI   bibtex
  19. Esser, Olivier. Inconsistency of the Axiom of Choice with the Positive Theory $GPK^+_\infty$. Journal of Symbolic Logic 65(4):1911--1916, Dec., 2000. www   DOI   bibtex
  20. Esser, Olivier. On the axiom of extensionality in the positive set theory. Mathematical Logic Quarterly 19:97--100, 2003. www   DOI   bibtex
  21. Evans, C D A and Hamkins, Joel David. Transfinite game values in infinite chess. (under review) www   arχiv   bibtex
  22. 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
  23. Forti, M and Hinnion, R. The Consistency Problem for Positive Comprehension Principles. J Symbolic Logic 54(4):1401--1418, 1989. bibtex
  24. 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
  25. Gitman, Victoria. Ramsey-like cardinals. The Journal of Symbolic Logic 76(2):519-540, 2011. www   arχiv   MR   bibtex
  26. Gitman, Victoria and Welch, Philip. Ramsey-like cardinals II. J Symbolic Logic 76(2):541--560, 2011. www   arχiv   MR   bibtex
  27. Gitman, Victoria and Johnstone, Thomas. Indestructibility for Ramsey and Ramsey-like cardinals. (In preparation) bibtex
  28. Goldblatt, Robert. Lectures on the Hyperreals. Springer, 1998. bibtex
  29. Goldstern, Martin and Shelah, Saharon. The Bounded Proper Forcing Axiom. J Symbolic Logic 60(1):58--73, 1995. www   bibtex
  30. Hamkins, Joel David and Lewis, Andy. Infinite time Turing machines. J Symbolic Logic 65(2):567--604, 2000. www   arχiv   DOI   MR   bibtex
  31. Hamkins, Joel David. Infinite time Turing machines. Minds and Machines 12(4):521--539, 2002. (special issue devoted to hypercomputation) www   arχiv   bibtex
  32. 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
  33. Hamkins, Joel David. The wholeness axioms and V=HOD. Arch Math Logic 40(1):1--8, 2001. www   arχiv   DOI   MR   bibtex
  34. Hamkins, Joel David. Tall cardinals. MLQ Math Log Q 55(1):68--86, 2009. www   DOI   MR   bibtex
  35. Hamkins, Joel David. Tall cardinals. MLQ Math Log Q 55(1):68--86, 2009. www   DOI   MR   bibtex
  36. Hamkins, Joel David. Unfoldable cardinals and the GCH. , 2008. www   bibtex
  37. Hamkins, Joel David and Johnstone, Thomas A. Resurrection axioms and uplifting cardinals. www   arχiv   bibtex
  38. Hamkins, Joel David and Johnstone, Thomas A. Strongly uplifting cardinals and the boldface resurrection axioms. www   arχiv   bibtex
  39. Donder, Hans-Dieter and Koepke, Peter. On the Consistency Strength of 'Accessible' Jónsson Cardinals and of the Weak Chang Conjecture. Annals of Pure and Applied Logic , 1998. www   DOI   bibtex
  40. Donder, Hans-Dieter and Levinski, Jean-Pierre. Some principles related to Chang's conjecture. Annals of Pure and Applied Logic , 1989. www   DOI   bibtex
  41. Hauser, Kai. Indescribable Cardinals and Elementary Embeddings. 56(2):439 - 457, 1991. www   DOI   bibtex
  42. Jackson, Steve; Ketchersid, Richard; Schlutzenberg, Farmer; Woodin, W Hugh. Determinacy and Jónsson cardinals in $L(\mathbb{R})$. , 2015. www   DOI   bibtex
  43. Jech, Thomas J. Set Theory. Third, Springer-Verlag, Berlin, 2003. (The third millennium edition, revised and expanded) www   bibtex
  44. Jensen, Ronald and Kunen, Kenneth. Some combinatorial properties of $L$ and $V$. Unpublished, 1969. www   bibtex
  45. 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
  46. 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
  47. 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
  48. Kentaro, Sato. Double helix in large large cardinals and iteration ofelementary embeddings. , 2007. www   bibtex
  49. Kunen, Kenneth. Saturated Ideals. J Symbolic Logic 43(1):65--76, 1978. www   bibtex
  50. Koellner, Peter and Woodin, W Hugh. Chapter 23: Large cardinals from Determinacy. Handbook of Set Theory , 2010. www   bibtex
  51. Larson, Paul B. A brief history of determinacy. , 2013. www   bibtex
  52. Laver, Richard. Implications between strong large cardinal axioms. Ann Math Logic 90(1--3):79--90, 1997. MR   bibtex
  53. Maddy, Penelope. Believing the axioms. I. J Symbolic Logic 53(2):181--511, 1988. www   DOI   bibtex
  54. Maddy, Penelope. Believing the axioms. II. J Symbolic Logic 53(3):736--764, 1988. www   DOI   bibtex
  55. Madore, David. A zoo of ordinals. , 2017. www   bibtex
  56. Mitchell, William J. Jónsson Cardinals, Erdős Cardinals, and the Core Model. J Symbol Logic , 1997. www   bibtex
  57. Mitchell, William J. The Covering Lemma. Handbook of Set Theory , 2001. www   bibtex
  58. Miyamoto, Tadatoshi. A note on weak segments of PFA. Proceedings of the sixth Asian logic conference pp. 175--197, 1998. bibtex
  59. Perlmutter, Norman. The large cardinals between supercompact and almost-huge. , 2010. www   bibtex
  60. Rathjen, Michael. The art of ordinal analysis. , 2006. www   bibtex
  61. 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
  62. Shelah, Saharon. Cardinal Arithmetic. Oxford Logic Guides 29, 1994. bibtex
  63. Schanker, Jason A. Partial near supercompactness. Ann Pure Appl Logic , 2012. (In Press.) www   DOI   bibtex
  64. Schanker, Jason A. Weakly measurable cardinals. MLQ Math Log Q 57(3):266--280, 2011. www   DOI   bibtex
  65. Schanker, Jason A. Weakly measurable cardinals and partial near supercompactness. Ph.D. Thesis, CUNY Graduate Center, 2011. bibtex
  66. Schindler, Ralf-Dieter. Proper forcing and remarkable cardinals. Bull Symbolic Logic 6(2):176--184, 2000. www   DOI   MR   bibtex
  67. Silver, Jack. A large cardinal in the constructible universe. Fund Math 69:93--100, 1970. MR   bibtex
  68. Silver, Jack. Some applications of model theory in set theory. Ann Math Logic 3(1):45--110, 1971. MR   bibtex
  69. Suzuki, Akira. Non-existence of generic elementary embeddings into the ground model. Tsukuba J Math 22(2):343--347, 1998. MR   bibtex | Abstract
  70. 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
  71. Trang, Nam and Wilson, Trevor. Determinacy from Strong Compactness of $\omega_1$. , 2016. www   bibtex
  72. Tryba, Jan. On Jónsson cardinals with uncountable cofinality. Israel Journal of Mathematics 49(4), 1983. bibtex
  73. 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
  74. Villaveces, Andrés. Chains of End Elementary Extensions of Models of Set Theory. JSTOR , 1996. www   bibtex
  75. Welch, Philip. Some remarks on the maximality of Inner Models. Logic Colloquium , 1998. www   bibtex
  76. Welch, Philip. The Lengths of Infinite Time Turing Machine Computations. Bulletin of the London Mathematical Society 32(2):129--136, 2000. bibtex
  77. Zapletal, Jindrich. A new proof of Kunen's inconsistency. Proc Amer Math Soc 124(7):2203--2204, 1996. www   MR   bibtex

User instructions

Cantor's attic users may make contributions to the library, in bibtex format, and then cite those references in other articles. Edit this page to make your contribution.