Difference between revisions of "Library"

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     AUTHOR = {Bagaria, Joan and Bosch, Roger},
 
     AUTHOR = {Bagaria, Joan and Bosch, Roger},
 
     TITLE = {Proper forcing extensions and Solovay models},
 
     TITLE = {Proper forcing extensions and Solovay models},
   JOURNAL = {Archive for Mathematical Logic}
+
   JOURNAL = {Archive for Mathematical Logic},
 
       YEAR = {2004},
 
       YEAR = {2004},
 
       DOI = {10.1007/s00153-003-0210-2},
 
       DOI = {10.1007/s00153-003-0210-2},
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#BagariaBosch2007:GenericAbsoluteness bibtex=@article {Bagaria2002:AxiomsOfGenericAbsoluteness,
 
#BagariaBosch2007:GenericAbsoluteness bibtex=@article {Bagaria2002:AxiomsOfGenericAbsoluteness,
 
     AUTHOR = {Bagaria, Joan and Bosch, Roger},
 
     AUTHOR = {Bagaria, Joan and Bosch, Roger},
     TITLE = {Generic absoluteness under projective forcing}
+
     TITLE = {Generic absoluteness under projective forcing},
   JOURNAL = {Fundamenta Mathematicae}
+
   JOURNAL = {Fundamenta Mathematicae},
 
       YEAR = {2007},
 
       YEAR = {2007},
 
     VOLUME = {194},
 
     VOLUME = {194},
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year = "1976"
 
year = "1976"
 
}
 
}
 
  
 
#Boney2017:ModelTheoreticCharacterizations bibtex=@article{BBoney2017:ModelTheoreticCharacterizations,
 
#Boney2017:ModelTheoreticCharacterizations bibtex=@article{BBoney2017:ModelTheoreticCharacterizations,
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   eprint = {1708.07561},
 
   eprint = {1708.07561},
 
}
 
}
    
+
 
 +
#Bosch2006:SmallDefinablyLargeCardinals bibtex=@article {Bosch2006:SmallDefinablyLargeCardinals,
 +
    AUTHOR = {Bosch, Roger},
 +
    TITLE = {Small Definably-large Cardinals},
 +
   JOURNAL = {Set Theory. Trends in Mathematics},
 +
      YEAR = {2006},
 +
    PAGES = {55-82},
 +
      DOI = {10.1007/3-7643-7692-9_3},
 +
      ISBN = {978-3-7643-7692-5},
 +
}
 +
 
 
#Cantor1915:ContributionsFoundingTransfinite bibtex=@book{Cantor1915:ContributionsFoundingTransfinite,  
 
#Cantor1915:ContributionsFoundingTransfinite bibtex=@book{Cantor1915:ContributionsFoundingTransfinite,  
 
   author = {Cantor, Georg},     
 
   author = {Cantor, Georg},     

Revision as of 13:21, 6 September 2019

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. Baaz, M and Papadimitriou, CH and Putnam, HW and Scott, DS and Harper, CL. Kurt Gödel and the Foundations of Mathematics: Horizons of Truth. Cambridge University Press, 2011. www   bibtex
  3. Bagaria, Joan. Axioms of generic absoluteness. Logic Colloquium 2002 , 2006. www   DOI   bibtex
  4. Bagaria, Joan and Bosch, Roger. Proper forcing extensions and Solovay models. Archive for Mathematical Logic , 2004. www   DOI   bibtex
  5. Bagaria, Joan and Bosch, Roger. Generic absoluteness under projective forcing. Fundamenta Mathematicae 194:95-120, 2007. DOI   bibtex
  6. Bagaria, Joan and Casacuberta, Carles and Mathias, A R D and Rosický, Jiří. Definable orthogonality classes in accessible categories are small. Journal of the European Mathematical Society 17(3):549--589. arχiv   bibtex
  7. Bagaria, Joan and Hamkins, Joel David and Tsaprounis, Konstantinos and Usuba, Toshimichi. Superstrong and other large cardinals are never Laver indestructible. Archive for Mathematical Logic 55(1-2):19--35, 2013. www   arχiv   DOI   bibtex
  8. Bagaria, Joan. Large Cardinals beyond Choice. , 2017. www   bibtex
  9. 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
  10. Blass, Andreas. Chapter 6: Cardinal characteristics of the continuum. Handbook of Set Theory , 2010. www   bibtex
  11. Blass, Andreas. Exact functors and measurable cardinals.. Pacific J Math 63(2):335--346, 1976. www   bibtex
  12. Boney, Will. Model Theoretic Characterizations of Large Cardinals. arχiv   bibtex
  13. Bosch, Roger. Small Definably-large Cardinals. Set Theory Trends in Mathematics pp. 55-82, 2006. DOI   bibtex
  14. Cantor, Georg. Contributions to the Founding of the Theory of Transfinite Numbers. Dover, New York, 1955. (Original year was 1915) www   bibtex
  15. Carmody, Erin Kathryn. Force to change large cardinal strength. , 2015. www   arχiv   bibtex
  16. Carmody, Erin and Gitman, Victoria and Habič, Miha E. A Mitchell-like order for Ramsey and Ramsey-like cardinals. , 2016. arχiv   bibtex
  17. 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. arχiv   bibtex
  18. Cody, Brent and Gitman, Victoria. Easton's theorem for Ramsey and strongly Ramsey cardinals. Annals of Pure and Applied Logic 166(9):934 - 952, 2015. www   DOI   bibtex
  19. Corazza, Paul. The Wholeness Axiom and Laver sequences. Annals of Pure and Applied Logic pp. 157--260, October, 2000. bibtex
  20. Corazza, Paul. The gap between ${\rm I}_3$ and the wholeness axiom. Fund Math 179(1):43--60, 2003. www   DOI   MR   bibtex
  21. Corazza, Paul. The Axiom of Infinity and transformations $j: V \to V$. Bulletin of Symbolic Logic 16(1):37--84, 2010. www   DOI   bibtex
  22. Dimonte, Vincenzo. I0 and rank-into-rank axioms. , 2017. arχiv   bibtex
  23. Dimopoulos, Stamatis. Woodin for strong compactness cardinals. The Journal of Symbolic Logic 84(1):301–319, 2019. arχiv   DOI   bibtex
  24. Dodd, Anthony and Jensen, Ronald. The core model. Ann Math Logic 20(1):43--75, 1981. www   DOI   MR   bibtex
  25. 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
  26. Donder, Hans-Dieter and Levinski, Jean-Pierre. Some principles related to Chang's conjecture. Annals of Pure and Applied Logic , 1989. www   DOI   bibtex
  27. Drake, Frank. Set Theory: An Introduction to Large Cardinals. North-Holland Pub. Co., 1974. bibtex
  28. 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
  29. Erdős, Paul and Hajnal, Andras. On the structure of set-mappings. Acta Math Acad Sci Hungar 9:111--131, 1958. MR   bibtex
  30. Eskrew, Monroe and Hayut, Yair. On the consistency of local and global versions of Chang's Conjecture. , 2016. arχiv   bibtex
  31. Esser, Olivier. Inconsistency of GPK+AFA. Mathematical Logic Quarterly 42:104--108, 1996. www   DOI   bibtex
  32. 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
  33. Esser, Olivier. On the Consistency of a Positive Theory. Mathematical Logic Quarterly 45:105--116, 1999. www   DOI   bibtex
  34. 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
  35. Esser, Olivier. On the axiom of extensionality in the positive set theory. Mathematical Logic Quarterly 19:97--100, 2003. www   DOI   bibtex
  36. Evans, C D A and Hamkins, Joel David. Transfinite game values in infinite chess. (under review) www   arχiv   bibtex
  37. Feng, Qi. A hierarchy of Ramsey cardinals. Annals of Pure and Applied Logic 49(3):257 - 277, 1990. DOI   bibtex
  38. 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
  39. Forti, M and Hinnion, R. The Consistency Problem for Positive Comprehension Principles. J Symbolic Logic 54(4):1401--1418, 1989. bibtex
  40. Friedman, Harvey M. Subtle cardinals and linear orderings. , 1998. www   bibtex
  41. Fuchs, Gunter and Hamkins, Joel David and Reitz, Jonas. Set-theoretic geology. Annals of Pure and Applied Logic 166(4):464 - 501, 2015. www   arχiv   DOI   bibtex
  42. 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
  43. Gitman, Victoria. Ramsey-like cardinals. The Journal of Symbolic Logic 76(2):519-540, 2011. www   arχiv   MR   bibtex
  44. Gitman, Victoria and Welch, Philip. Ramsey-like cardinals II. J Symbolic Logic 76(2):541--560, 2011. www   arχiv   MR   bibtex
  45. Gitman, Victoria and Johnstone, Thomas A. Indestructibility for Ramsey and Ramsey-like cardinals. (In preparation) www   bibtex
  46. Gitman, Victoria and Shindler, Ralf. Virtual large cardinals. www   bibtex
  47. Goldblatt, Robert. Lectures on the Hyperreals. Springer, 1998. bibtex
  48. Goldstern, Martin and Shelah, Saharon. The Bounded Proper Forcing Axiom. J Symbolic Logic 60(1):58--73, 1995. www   bibtex
  49. Hamkins, Joel David and Lewis, Andy. Infinite time Turing machines. J Symbolic Logic 65(2):567--604, 2000. www   arχiv   DOI   MR   bibtex
  50. Hamkins, Joel David. The wholeness axioms and V=HOD. Arch Math Logic 40(1):1--8, 2001. www   arχiv   DOI   MR   bibtex
  51. Hamkins, Joel David. Infinite time Turing machines. Minds and Machines 12(4):521--539, 2002. (special issue devoted to hypercomputation) www   arχiv   bibtex
  52. 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
  53. Hamkins, Joel David. Unfoldable cardinals and the GCH. , 2008. arχiv   bibtex
  54. Hamkins, Joel David. Tall cardinals. MLQ Math Log Q 55(1):68--86, 2009. www   DOI   MR   bibtex
  55. Hamkins, Joel David and Johnstone, Thomas A. Indestructible strong un-foldability. Notre Dame J Form Log 51(3):291--321, 2010. bibtex
  56. Hamkins, Joel David and Johnstone, Thomas A. Resurrection axioms and uplifting cardinals. , 2014. www   arχiv   bibtex
  57. Hamkins, Joel David and Johnstone, Thomas A. Strongly uplifting cardinals and the boldface resurrection axioms. , 2014. arχiv   bibtex
  58. Hauser, Kai. Indescribable Cardinals and Elementary Embeddings. 56(2):439 - 457, 1991. www   DOI   bibtex
  59. Holy, Peter and Schlicht, Philipp. A hierarchy of Ramsey-like cardinals. Fundamenta Mathematicae 242:49-74, 2018. www   arχiv   DOI   bibtex
  60. Jackson, Steve; Ketchersid, Richard; Schlutzenberg, Farmer; Woodin, W Hugh. Determinacy and Jónsson cardinals in $L(\mathbb{R})$. , 2015. arχiv   DOI   bibtex
  61. Jech, Thomas J. Set Theory. Third, Springer-Verlag, Berlin, 2003. (The third millennium edition, revised and expanded) www   bibtex
  62. Jensen, Ronald and Kunen, Kenneth. Some combinatorial properties of $L$ and $V$. Unpublished, 1969. www   bibtex
  63. 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
  64. 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
  65. Kanamori, Akihiro and Awerbuch-Friedlander, Tamara. The compleat 0†. Mathematical Logic Quarterly 36(2):133-141, 1990. DOI   bibtex
  66. 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
  67. Kentaro, Sato. Double helix in large large cardinals and iteration ofelementary embeddings. , 2007. www   bibtex
  68. Kunen, Kenneth. Saturated Ideals. J Symbolic Logic 43(1):65--76, 1978. www   bibtex
  69. Koellner, Peter and Woodin, W Hugh. Chapter 23: Large cardinals from Determinacy. Handbook of Set Theory , 2010. www   bibtex
  70. Larson, Paul B. A brief history of determinacy. , 2013. www   bibtex
  71. Laver, Richard. Implications between strong large cardinal axioms. Ann Math Logic 90(1--3):79--90, 1997. MR   bibtex
  72. Leshem, Amir. On the consistency of the definable tree property on $\aleph_1$. J Symbolic Logic 65(3):1204-1214, 2000. arχiv   DOI   bibtex
  73. Maddy, Penelope. Believing the axioms. I. J Symbolic Logic 53(2):181--511, 1988. www   DOI   bibtex
  74. Maddy, Penelope. Believing the axioms. II. J Symbolic Logic 53(3):736--764, 1988. www   DOI   bibtex
  75. Madore, David. A zoo of ordinals. , 2017. www   bibtex
  76. Makowsky, Johann. Vopěnka's Principle and Compact Logics. J Symbol Logic www   bibtex
  77. Mitchell, William J. Jónsson Cardinals, Erdős Cardinals, and the Core Model. J Symbol Logic , 1997. arχiv   bibtex
  78. Mitchell, William J. The Covering Lemma. Handbook of Set Theory , 2001. www   bibtex
  79. Miyamoto, Tadatoshi. A note on weak segments of PFA. Proceedings of the sixth Asian logic conference pp. 175--197, 1998. bibtex
  80. Nielsen, Dan Saattrup and Welch, Philip. Games and Ramsey-like cardinals. , 2018. arχiv   bibtex
  81. Perlmutter, Norman. The large cardinals between supercompact and almost-huge. , 2010. arχiv   bibtex
  82. Rathjen, Michael. The art of ordinal analysis. , 2006. www   bibtex
  83. Schanker, Jason A. Partial near supercompactness. Ann Pure Appl Logic , 2012. (In Press.) www   DOI   bibtex
  84. Schanker, Jason A. Weakly measurable cardinals. MLQ Math Log Q 57(3):266--280, 2011. www   DOI   bibtex
  85. Schanker, Jason A. Weakly measurable cardinals and partial near supercompactness. Ph.D. Thesis, CUNY Graduate Center, 2011. bibtex
  86. Schindler, Ralf-Dieter. Proper forcing and remarkable cardinals. Bull Symbolic Logic 6(2):176--184, 2000. www   DOI   MR   bibtex
  87. 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
  88. Shelah, Saharon. Cardinal Arithmetic. Oxford Logic Guides 29, 1994. bibtex
  89. Silver, Jack. A large cardinal in the constructible universe. Fund Math 69:93--100, 1970. MR   bibtex
  90. Silver, Jack. Some applications of model theory in set theory. Ann Math Logic 3(1):45--110, 1971. MR   bibtex
  91. Suzuki, Akira. Non-existence of generic elementary embeddings into the ground model. Tsukuba J Math 22(2):343--347, 1998. MR   bibtex | Abstract
  92. 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
  93. Trang, Nam and Wilson, Trevor. Determinacy from Strong Compactness of $\omega_1$. , 2016. arχiv   bibtex
  94. Tryba, Jan. On Jónsson cardinals with uncountable cofinality. Israel Journal of Mathematics 49(4), 1983. bibtex
  95. Usuba, Toshimichi. The downward directed grounds hypothesis and very large cardinals. Journal of Mathematical Logic 17(02):1750009, 2017. arχiv   DOI   bibtex
  96. Usuba, Toshimichi. Extendible cardinals and the mantle. Archive for Mathematical Logic 58(1-2):71-75, 2019. arχiv   DOI   bibtex
  97. 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
  98. Villaveces, Andrés. Chains of End Elementary Extensions of Models of Set Theory. JSTOR , 1996. arχiv   bibtex
  99. Welch, Philip. Some remarks on the maximality of Inner Models. Logic Colloquium , 1998. www   bibtex
  100. Welch, Philip. The Lengths of Infinite Time Turing Machine Computations. Bulletin of the London Mathematical Society 32(2):129--136, 2000. bibtex
  101. Woodin, W Hugh. Suitable extender models I. Journal of Mathematical Logic 10(01n02):101-339, 2010. www   DOI   bibtex
  102. Woodin, W Hugh. Suitable extender models II: beyond $\omega$-huge. Journal of Mathematical Logic 11(02):115-436, 2011. www   DOI   bibtex
  103. Zapletal, Jindrich. A new proof of Kunen's inconsistency. Proc Amer Math Soc 124(7):2203--2204, 1996. www   DOI   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.