# Difference between revisions of "Library"

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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. Apter, Arthur W. Some applications of Sargsyan’s equiconsistency method. Fund Math 216:207--222. bibtex
3. =@paper{Arai97, title={A sneak preview of proof theory of ordinals}, author={Arai, Toshiyasu} url={https://www.arxiv.org/abs/1102.0596v1} year={1997}}
4. 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
5. Bagaria, Joan. Axioms of generic absoluteness. Logic Colloquium 2002 , 2006. www   DOI   bibtex
6. Bagaria, Joan and Bosch, Roger. Proper forcing extensions and Solovay models. Archive for Mathematical Logic , 2004. www   DOI   bibtex
7. Bagaria, Joan and Bosch, Roger. Generic absoluteness under projective forcing. Fundamenta Mathematicae 194:95-120, 2007. DOI   bibtex
8. Bagaria, Joan. $C^{(n)}$-cardinals. Archive for Mathematical Logic 51(3--4):213--240, 2012. www   arχiv   DOI   bibtex
9. 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
10. 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
11. Bagaria, Joan. Large Cardinals beyond Choice. , 2017. www   bibtex
12. Bagaria, Joan and Gitman, Victoria and Schindler, Ralf. Generic {V}opěnka's {P}rinciple, remarkable cardinals, and the weak {P}roper {F}orcing {A}xiom. Arch Math Logic 56(1-2):1--20, 2017. www   DOI   MR   bibtex
13. Bagaria, Joan and Koellner, Peter and Woodin, W Hugh. Large Cardinals beyond Choice. Bulletin of Symbolic Logic 25(3):283--318, 2019. www   DOI   bibtex
14. 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
15. Blass, Andreas. Chapter 6: Cardinal characteristics of the continuum. Handbook of Set Theory , 2010. www   bibtex
16. Blass, Andreas. Exact functors and measurable cardinals.. Pacific J Math 63(2):335--346, 1976. www   bibtex
17. Boney, Will. Model Theoretic Characterizations of Large Cardinals. arχiv   bibtex
18. Bosch, Roger. Small Definably-large Cardinals. Set Theory Trends in Mathematics pp. 55-82, 2006. DOI   bibtex
19. Cantor, Georg. Contributions to the Founding of the Theory of Transfinite Numbers. Dover, New York, 1955. (Original year was 1915) www   bibtex
20. Carmody, Erin Kathryn. Force to change large cardinal strength. , 2015. www   arχiv   bibtex
21. Carmody, Erin and Gitman, Victoria and Habič, Miha E. A Mitchell-like order for Ramsey and Ramsey-like cardinals. , 2016. arχiv   bibtex
22. 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
23. 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
24. Corazza, Paul. The Wholeness Axiom and Laver sequences. Annals of Pure and Applied Logic pp. 157--260, October, 2000. bibtex
25. Corazza, Paul. The gap between $\mathrm{I}_3$ and the wholeness axiom. Fund Math 179(1):43--60, 2003. www   DOI   MR   bibtex
26. Corazza, Paul. The spectrum of elementary embeddings $j : V \to V$. Annals of Pure and Applied Logic 139(1--3):327-399, May, 2006. DOI   bibtex
27. Corazza, Paul. The Axiom of Infinity and transformations $j: V \to V$. Bulletin of Symbolic Logic 16(1):37--84, 2010. www   DOI   bibtex
28. Daghighi, Ali Sadegh and Pourmahdian, Massoud. On Some Properties of Shelah Cardinals. Bull Iran Math Soc 44(5):1117-1124, October, 2018. www   DOI   bibtex
29. Dimonte, Vincenzo. I0 and rank-into-rank axioms. , 2017. arχiv   bibtex
30. Dimopoulos, Stamatis. Woodin for strong compactness cardinals. The Journal of Symbolic Logic 84(1):301–319, 2019. arχiv   DOI   bibtex
31. Dodd, Anthony and Jensen, Ronald. The core model. Ann Math Logic 20(1):43--75, 1981. www   DOI   MR   bibtex
32. 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
33. Donder, Hans-Dieter and Levinski, Jean-Pierre. Some principles related to Chang's conjecture. Annals of Pure and Applied Logic 45:39-101, 1989. www   DOI   bibtex
34. Drake, Frank. Set Theory: An Introduction to Large Cardinals. North-Holland Pub. Co., 1974. bibtex
35. Enayat, Ali. Models of set theory with definable ordinals. Archive for Mathematical Logic 44:363–385, April, 2005. www   DOI   bibtex
36. 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
37. Erdős, Paul and Hajnal, Andras. On the structure of set-mappings. Acta Math Acad Sci Hungar 9:111--131, 1958. MR   bibtex
38. Eskrew, Monroe and Hayut, Yair. On the consistency of local and global versions of Chang's Conjecture. , 2016. arχiv   bibtex
39. Esser, Olivier. Inconsistency of GPK+AFA. Mathematical Logic Quarterly 42:104--108, 1996. www   DOI   bibtex
40. 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
41. Esser, Olivier. On the Consistency of a Positive Theory. Mathematical Logic Quarterly 45:105--116, 1999. www   DOI   bibtex
42. 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
43. Esser, Olivier. On the axiom of extensionality in the positive set theory. Mathematical Logic Quarterly 19:97--100, 2003. www   DOI   bibtex
44. Evans, C D A and Hamkins, Joel David. Transfinite game values in infinite chess. (under review) www   arχiv   bibtex
45. Feng, Qi. A hierarchy of Ramsey cardinals. Annals of Pure and Applied Logic 49(3):257 - 277, 1990. DOI   bibtex
46. 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
47. Forti, M and Hinnion, R. The Consistency Problem for Positive Comprehension Principles. J Symbolic Logic 54(4):1401--1418, 1989. bibtex
48. Friedman, Harvey M. Subtle cardinals and linear orderings. , 1998. www   bibtex
49. 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
50. 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
51. Gitman, Victoria. Ramsey-like cardinals. The Journal of Symbolic Logic 76(2):519-540, 2011. www   arχiv   MR   bibtex
52. Gitman, Victoria and Welch, Philip. Ramsey-like cardinals II. J Symbolic Logic 76(2):541--560, 2011. www   arχiv   MR   bibtex
53. Gitman, Victoria and Hamkins, Joel David. A model of the generic Vopěnka principle in which the ordinals are not Mahlo. , 2018. arχiv   bibtex
54. Gitman, Victoria and Johnstone, Thomas A. Indestructibility for Ramsey and Ramsey-like cardinals. (In preparation) www   bibtex
55. Gitman, Victoria and Shindler, Ralf. Virtual large cardinals. www   bibtex
56. Goldblatt, Robert. Lectures on the Hyperreals. Springer, 1998. bibtex
57. Goldstern, Martin and Shelah, Saharon. The Bounded Proper Forcing Axiom. J Symbolic Logic 60(1):58--73, 1995. www   bibtex
58. Golshani, Mohammad. An Easton like theorem in the presence of Shelah cardinals. M Arch Math Logic 56(3-4):273-287, May, 2017. www   DOI   bibtex
59. Hamkins, Joel David and Lewis, Andy. Infinite time Turing machines. J Symbolic Logic 65(2):567--604, 2000. www   arχiv   DOI   MR   bibtex
60. Hamkins, Joel David. The wholeness axioms and V=HOD. Arch Math Logic 40(1):1--8, 2001. www   arχiv   DOI   MR   bibtex
61. Hamkins, Joel David. Infinite time Turing machines. Minds and Machines 12(4):521--539, 2002. (special issue devoted to hypercomputation) www   arχiv   bibtex
62. 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
63. Hamkins, Joel David. Unfoldable cardinals and the GCH. , 2008. arχiv   bibtex
64. Hamkins, Joel David. Tall cardinals. MLQ Math Log Q 55(1):68--86, 2009. www   DOI   MR   bibtex
65. Hamkins, Joel David and Johnstone, Thomas A. Indestructible strong un-foldability. Notre Dame J Form Log 51(3):291--321, 2010. bibtex
66. Hamkins, Joel David; Linetsky, David; Reitz, Jonas. Pointwise Definable Models of Set Theory. , 2012. arχiv   bibtex
67. Hamkins, Joel David and Johnstone, Thomas A. Resurrection axioms and uplifting cardinals. , 2014. www   arχiv   bibtex
68. Hamkins, Joel David and Johnstone, Thomas A. Strongly uplifting cardinals and the boldface resurrection axioms. , 2014. arχiv   bibtex
69. Hamkins, Joel David. The Vopěnka principle is inequivalent to but conservative over the Vopěnka scheme. , 2016. www   arχiv   bibtex
70. Hauser, Kai. Indescribable Cardinals and Elementary Embeddings. 56(2):439 - 457, 1991. www   DOI   bibtex
71. Holy, Peter and Schlicht, Philipp. A hierarchy of Ramsey-like cardinals. Fundamenta Mathematicae 242:49-74, 2018. www   arχiv   DOI   bibtex
72. Jackson, Steve; Ketchersid, Richard; Schlutzenberg, Farmer; Woodin, W Hugh. Determinacy and Jónsson cardinals in $L(\mathbb{R})$. , 2015. arχiv   DOI   bibtex
73. Jech, Thomas J. Set Theory. Third, Springer-Verlag, Berlin, 2003. (The third millennium edition, revised and expanded) www   bibtex
74. Jensen, Ronald and Kunen, Kenneth. Some combinatorial properties of $L$ and $V$. Unpublished, 1969. www   bibtex
75. 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
76. 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
77. Kanamori, Akihiro and Awerbuch-Friedlander, Tamara. The compleat 0†. Mathematical Logic Quarterly 36(2):133-141, 1990. DOI   bibtex
78. 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
79. Kentaro, Sato. Double helix in large large cardinals and iteration of elementary embeddings. Annals of Pure and Applied Logic 146(2-3):199-236, May, 2007. www   DOI   bibtex
80. Ketonen, Jussi. Some combinatorial principles. Trans Amer Math Soc 188:387-394, 1974. DOI   bibtex
81. Koellner, Peter and Woodin, W Hugh. Chapter 23: Large cardinals from Determinacy. Handbook of Set Theory , 2010. www   bibtex
82. Kunen, Kenneth. Saturated Ideals. J Symbolic Logic 43(1):65--76, 1978. www   bibtex
83. Larson, Paul B. A brief history of determinacy. , 2013. www   bibtex
84. Laver, Richard. Implications between strong large cardinal axioms. Ann Math Logic 90(1--3):79--90, 1997. MR   bibtex
85. Leshem, Amir. On the consistency of the definable tree property on $\aleph_1$. J Symbolic Logic 65(3):1204-1214, 2000. arχiv   DOI   bibtex
86. Maddy, Penelope. Believing the axioms. I. J Symbolic Logic 53(2):181--511, 1988. www   DOI   bibtex
87. Maddy, Penelope. Believing the axioms. II. J Symbolic Logic 53(3):736--764, 1988. www   DOI   bibtex
88. Madore, David. A zoo of ordinals. , 2017. www   bibtex
89. Makowsky, Johann. Vopěnka's Principle and Compact Logics. J Symbol Logic , 1985. www   bibtex
90. Marek, W. Stable sets, a characterization of $β_2$-models of full second order arithmetic and some related facts. Fundamenta Mathematicae 82(2):175-189, 1974. www   bibtex
91. Mitchell, William J. Jónsson Cardinals, Erdős Cardinals, and the Core Model. J Symbol Logic , 1997. arχiv   bibtex
92. Mitchell, William J. The Covering Lemma. Handbook of Set Theory , 2001. www   bibtex
93. Miyamoto, Tadatoshi. A note on weak segments of PFA. Proceedings of the sixth Asian logic conference pp. 175--197, 1998. bibtex
94. Nielsen, Dan Saattrup and Welch, Philip. Games and Ramsey-like cardinals. , 2018. arχiv   bibtex
95. Perlmutter, Norman. The large cardinals between supercompact and almost-huge. , 2010. www   arχiv   bibtex
96. Rathjen, Michael. The art of ordinal analysis. , 2006. www   bibtex
97. Schanker, Jason A. Partial near supercompactness. Ann Pure Appl Logic , 2012. (In Press.) www   DOI   bibtex
98. Schanker, Jason A. Weakly measurable cardinals. MLQ Math Log Q 57(3):266--280, 2011. www   DOI   bibtex
99. Schanker, Jason A. Weakly measurable cardinals and partial near supercompactness. Ph.D. Thesis, CUNY Graduate Center, 2011. bibtex
100. Schimmerling, Ernest. Woodin cardinals, Shelah cardinals, and the Mitchell-Steel core model. Proc Amer Math Soc 130(11):3385-3391, 2002. DOI   bibtex
101. Schindler, Ralf-Dieter. Proper forcing and remarkable cardinals. Bull Symbolic Logic 6(2):176--184, 2000. www   DOI   MR   bibtex
102. 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
103. Shelah, Saharon. Cardinal Arithmetic. Oxford Logic Guides 29, 1994. bibtex
104. Silver, Jack. A large cardinal in the constructible universe. Fund Math 69:93--100, 1970. MR   bibtex
105. Silver, Jack. Some applications of model theory in set theory. Ann Math Logic 3(1):45--110, 1971. MR   bibtex
106. Suzuki, Akira. Non-existence of generic elementary embeddings into the ground model. Tsukuba J Math 22(2):343--347, 1998. MR   bibtex | Abstract
107. 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
108. Trang, Nam and Wilson, Trevor. Determinacy from Strong Compactness of $\omega_1$. , 2016. arχiv   bibtex
109. Tryba, Jan. On Jónsson cardinals with uncountable cofinality. Israel Journal of Mathematics 49(4), 1983. bibtex
110. Usuba, Toshimichi. The downward directed grounds hypothesis and very large cardinals. Journal of Mathematical Logic 17(02):1750009, 2017. arχiv   DOI   bibtex
111. Usuba, Toshimichi. Extendible cardinals and the mantle. Archive for Mathematical Logic 58(1-2):71-75, 2019. arχiv   DOI   bibtex
112. 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
113. Villaveces, Andrés. Chains of End Elementary Extensions of Models of Set Theory. JSTOR , 1996. arχiv   bibtex
114. Welch, Philip. Some remarks on the maximality of Inner Models. Logic Colloquium , 1998. www   bibtex
115. Welch, Philip. The Lengths of Infinite Time Turing Machine Computations. Bulletin of the London Mathematical Society 32(2):129--136, 2000. bibtex
116. Wilson, Trevor M. Weakly remarkable cardinals, Erdős cardinals, and the generic Vopěnka principle. , 2018. arχiv   bibtex
117. Woodin, W Hugh. Suitable extender models I. Journal of Mathematical Logic 10(01n02):101-339, 2010. www   DOI   bibtex
118. Woodin, W Hugh. Suitable extender models II: beyond $\omega$-huge. Journal of Mathematical Logic 11(02):115-436, 2011. www   DOI   bibtex
119. Zapletal, Jindrich. A new proof of Kunen's inconsistency. Proc Amer Math Soc 124(7):2203--2204, 1996. www   DOI   MR   bibtex

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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.