The Cantor's attic library

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

Library holdings

1. Abramson, F., Harrington, L., Kleinberg, E., & Zwicker, W. (1977). Flipping properties: a unifying thread in the theory of large cardinals. Ann. Math. Logic, 12(1), 25–58.
2. Apter, A. W. Some applications of Sargsyan’s equiconsistency method. Fund. Math., 216, 207–222.
3. Baaz, M., Papadimitriou, C. H., Putnam, H. W., Scott, D. S., & Harper, C. L. (2011). Kurt Gödel and the Foundations of Mathematics: Horizons of Truth. Cambridge University Press. https://books.google.pl/books?id=Tg0WXU5_8EgC
4. Bagaria, J. (2006). Axioms of generic absoluteness. Logic Colloquium 2002. https://doi.org/10.1201/9781439865903
5. Bagaria, J., & Bosch, R. (2004). Proper forcing extensions and Solovay models. Archive for Mathematical Logic. https://doi.org/10.1007/s00153-003-0210-2
6. Bagaria, J., & Bosch, R. (2007). Generic absoluteness under projective forcing. Fundamenta Mathematicae, 194, 95–120. https://doi.org/10.4064/fm194-2-1
7. Bagaria, J. (2012). \(C^{(n)}\)-cardinals. Archive for Mathematical Logic, 51(3–4), 213–240. https://doi.org/10.1007/s00153-011-0261-8
8. Bagaria, J., Casacuberta, C., Mathias, A. R. D., & Rosický, J. Definable orthogonality classes in accessible categories are small. Journal of the European Mathematical Society, 17(3), 549–589.
9. Bagaria, J., Hamkins, J. D., Tsaprounis, K., & Usuba, T. (2013). Superstrong and other large cardinals are never Laver indestructible. Archive for Mathematical Logic, 55(1-2), 19–35. https://doi.org/10.1007/s00153-015-0458-3
10. Bagaria, J. (2017). Large Cardinals beyond Choice. https://events.math.unipd.it/aila2017/sites/default/files/BAGARIA.pdf
11. Bagaria, J., Gitman, V., & Schindler, R. (2017). Generic Vopěnkaś Principle, remarkable cardinals, and the weak Proper Forcing Axiom. Arch. Math. Logic, 56(1-2), 1–20. https://doi.org/10.1007/s00153-016-0511-x
12. Baumgartner, J. (1975). Ineffability properties of cardinals. I. In 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). North-Holland.
13. Blass, A. (2010). Chapter 6: Cardinal characteristics of the continuum. Handbook of Set Theory. http://www.math.lsa.umich.edu/ ablass/hbk.pdf
14. Blass, A. (1976). Exact functors and measurable cardinals. Pacific J. Math., 63(2), 335–346. http://web.archive.org/web/20191116153209/https://projecteuclid.org:443/euclid.pjm/1102867389
15. Boney, W. (2017). Model Theoretic Characterizations of Large Cardinals.
16. Bosch, R. (2006). Small Definably-large Cardinals. Set Theory. Trends in Mathematics, 55–82. https://doi.org/10.1007/3-7643-7692-9_3
17. Cantor, G. (1955). Contributions to the Founding of the Theory of Transfinite Numbers (P. Jourdain, Ed.). Dover. http://www.archive.org/details/contributionstot003626mbp
18. Carmody, E. K. (2015). Force to change large cardinal strength. https://academicworks.cuny.edu/gc_etds/879/
19. Carmody, E., Gitman, V., & Habič, M. E. (2016). A Mitchell-like order for Ramsey and Ramsey-like cardinals.
20. Chang, C. C. (1971). Sets Constructible Using \(\mathcal {L}_{κ,κ}\). In Axiomatic set theory (Proc. Sympos. Pure Math., Vol. XIII, Part I, Univ. California, Los Angeles, Calif., 1967) (pp. 1–8). Amer. Math. Soc.
21. Cody, B., Gitik, M., Hamkins, J. D., & Schanker, J. (2013). The Least Weakly Compact Cardinal Can Be Unfoldable, Weakly Measurable and Nearly θ-Supercompact.
22. Cody, B., & Gitman, V. (2015). Eastonś theorem for Ramsey and strongly Ramsey cardinals. Annals of Pure and Applied Logic, 166(9), 934–952. https://doi.org/10.1016/j.apal.2015.04.006
23. Corazza, P. (2000). The Wholeness Axiom and Laver sequences. Annals of Pure and Applied Logic, 157–260.
24. Corazza, P. (2003). The gap between \({\rm I}_3\)and the wholeness axiom. Fund. Math., 179(1), 43–60. https://doi.org/10.4064/fm179-1-4
25. Corazza, P. (2006). The spectrum of elementary embeddings j : V \to V. Annals of Pure and Applied Logic, 139(1–3), 327–399. https://doi.org/10.1016/j.apal.2005.06.014
26. Corazza, P. (2010). The Axiom of Infinity and transformations j: V \to V. Bulletin of Symbolic Logic, 16(1), 37–84. https://doi.org/10.2178/bsl/1264433797
27. Daghighi, A. S., & Pourmahdian, M. (2018). On Some Properties of Shelah Cardinals. Bull. Iran. Math. Soc., 44(5), 1117–1124. https://doi.org/10.1007/s41980-018-0075-0
28. Dimonte, V. (2017). I0 and rank-into-rank axioms.
29. Dimopoulos, S. (2019). Woodin for strong compactness cardinals. The Journal of Symbolic Logic, 84(1), 301–319. https://doi.org/10.1017/jsl.2018.67
30. Dodd, A., & Jensen, R. (1981). The core model. Ann. Math. Logic, 20(1), 43–75. https://doi.org/10.1016/0003-4843(81)90011-5
31. Donder, H.-D., & Koepke, P. (1998). On the Consistency Strength of Áccessible\’Jónsson Cardinals and of the Weak Chang Conjecture. Annals of Pure and Applied Logic. https://doi.org/10.1016/0168-0072(83)90020-9
32. Donder, H.-D., & Levinski, J.-P. (1989). Some principles related to Changś conjecture. Annals of Pure and Applied Logic. https://doi.org/10.1016/0168-0072(89)90030-4
33. Drake, F. (1974). Set Theory: An Introduction to Large Cardinals. North-Holland Pub. Co.
34. Erdős, P., & Hajnal, A. (1962). Some remarks concerning our paper “On the structure of set-mappings\’\’. Non-existence of a two-valued σ-measure for the first uncountable inaccessible cardinal. Acta Math. Acad. Sci. Hungar., 13, 223–226.
35. Erdős, P., & Hajnal, A. (1958). On the structure of set-mappings. Acta Math. Acad. Sci. Hungar, 9, 111–131.
36. Eskrew, M., & Hayut, Y. (2016). On the consistency of local and global versions of Changś Conjecture.
37. Esser, O. (1996). Inconsistency of GPK+AFA. Mathematical Logic Quarterly, 42, 104–108. https://doi.org/10.1002/malq.19960420109
38. Esser, O. (1997). An Interpretation of the Zermelo-Fraenkel Set Theory and the Kelley-Morse Set Theory in a Positive Theory. Mathematical Logic Quarterly, 43, 369–377. https://doi.org/10.1002/malq.19970430309
39. Esser, O. (1999). On the Consistency of a Positive Theory. Mathematical Logic Quarterly, 45, 105–116. https://doi.org/10.1002/malq.19990450110
40. Esser, O. (2000). Inconsistency of the Axiom of Choice with the Positive Theory GPK^+_∞. Journal of Symbolic Logic, 65(4), 1911–1916. https://doi.org/10.2307/2695086
41. Esser, O. (2003). On the axiom of extensionality in the positive set theory. Mathematical Logic Quarterly, 19, 97–100. https://doi.org/10.1002/malq.200310009
42. Evans, C. D. A., & Hamkins, J. D. Transfinite game values in infinite chess. http://jdh.hamkins.org/game-values-in-infinite-chess
43. Feng, Q. (1990). A hierarchy of Ramsey cardinals. Annals of Pure and Applied Logic, 49(3), 257–277. https://doi.org/10.1016/0168-0072(90)90028-Z
44. Foreman, M., & Kanamori, A. (2010). Handbook of Set Theory (M. Foreman & A. Kanamori, Eds.; First). Springer. http://www.springer.com/mathematics/book/978-1-4020-4843-2
45. Forti, M., & Hinnion, R. (1989). The Consistency Problem for Positive Comprehension Principles. J. Symbolic Logic, 54(4), 1401–1418.
46. Friedman, H. M. (1998). Subtle cardinals and linear orderings. https://u.osu.edu/friedman.8/files/2014/01/subtlecardinals-1tod0i8.pdf
47. Fuchs, G., Hamkins, J. D., & Reitz, J. (2015). Set-theoretic geology. Annals of Pure and Applied Logic, 166(4), 464–501. https://doi.org/http://web.archive.org/web/20191116153209/https://doi.org/10.1016/j.apal.2014.11.004
48. Gaifman, H. (1974). Elementary embeddings of models of set-theory and certain subtheories. In Axiomatic set theory (Proc. Sympos. Pure Math., Vol. XIII, Part II, Univ. California, Los Angeles, Calif., 1967) (pp. 33–101). Amer. Math. Soc.
49. Gitman, V. (2011). Ramsey-like cardinals. The Journal of Symbolic Logic, 76(2), 519–540. http://boolesrings.org/victoriagitman/files/2011/08/ramseylikecardinals.pdf
50. Gitman, V., & Welch, P. (2011). Ramsey-like cardinals II. J. Symbolic Logic, 76(2), 541–560. http://boolesrings.org/victoriagitman/files/2011/08/ramseylikecardinalsii.pdf
51. Gitman, V., & Hamkins, J. D. (2018). A model of the generic Vopěnka principle in which the ordinals are not Mahlo.
52. Gitman, V., & Johnstone, T. A. Indestructibility for Ramsey and Ramsey-like cardinals. https://victoriagitman.github.io/files/indestructibleramseycardinalsnew.pdf
53. Gitman, V., & Shindler, R. Virtual large cardinals. https://ivv5hpp.uni-muenster.de/u/rds/virtualLargeCardinalsEdited5.pdf
54. Goldblatt, R. (1998). Lectures on the Hyperreals. Springer.
55. Goldstern, M., & Shelah, S. (1995). The Bounded Proper Forcing Axiom. J. Symbolic Logic, 60(1), 58–73. http://www.jstor.org/stable/2275509
56. Golshani, M. (2017). An Easton like theorem in the presence of Shelah cardinals. M. Arch. Math. Logic, 56(3-4), 273–287. https://doi.org/10.1007/s00153-017-0528-9
57. Hamkins, J. D., & Lewis, A. (2000). Infinite time Turing machines. J. Symbolic Logic, 65(2), 567–604. https://doi.org/10.2307/2586556
58. Hamkins, J. D. (2001). The wholeness axioms and V=HOD. Arch. Math. Logic, 40(1), 1–8. https://doi.org/10.1007/s001530050169
59. Hamkins, J. D. (2002). Infinite time Turing machines. Minds and Machines, 12(4), 521–539. http://boolesrings.org/hamkins/turing-mm/
60. Hamkins, J. D. (2004). Supertask computation. Classical and New Paradigms of Computation and Their Complexity Hierarchies, 23, 141–158. https://doi.org/10.1007/978-1-4020-2776-5_8
61. Hamkins, J. D. (2008). Unfoldable cardinals and the GCH.
62. Hamkins, J. D. (2009). Tall cardinals. MLQ Math. Log. Q., 55(1), 68–86. https://doi.org/10.1002/malq.200710084
63. Hamkins, J. D., & Johnstone, T. A. (2010). Indestructible strong un-foldability. Notre Dame J. Form. Log., 51(3), 291–321.
64. Hamkins, J. D., & Johnstone, T. A. (2014). Resurrection axioms and uplifting cardinals. http://jdh.hamkins.org/resurrection-axioms-and-uplifting-cardinals/
65. Hamkins, J. D., & Johnstone, T. A. (2014). Strongly uplifting cardinals and the boldface resurrection axioms.
66. Hamkins, J. D. (2016). The Vopěnka principle is inequivalent to but conservative over the Vopěnka scheme. http://jdh.hamkins.org/vopenka-principle-vopenka-scheme/
67. Hauser, K. (1991). Indescribable Cardinals and Elementary Embeddings. 56(2), 439–457. https://doi.org/10.2307/2274692
68. Holy, P., & Schlicht, P. (2018). A hierarchy of Ramsey-like cardinals. Fundamenta Mathematicae, 242, 49–74. https://doi.org/10.4064/fm396-9-2017
69. Jackson, S., Ketchersid, R., Schlutzenberg, F., & Woodin, W. H. (2015). Determinacy and Jónsson cardinals in L(\mathbbR). https://doi.org/10.1017/jsl.2014.49
70. Jech, T. J. (2003). Set Theory (Third). Springer-Verlag. https://logic.wikischolars.columbia.edu/file/view/Jech%2C+T.+J.+%282003%29.+Set+Theory+%28The+3rd+millennium+ed.%29.pdf
71. Jensen, R., & Kunen, K. (1969). Some combinatorial properties of L and V. http://www.mathematik.hu-berlin.de/ raesch/org/jensen.html
72. Kanamori, A., & Magidor, M. (1978). The evolution of large cardinal axioms in set theory. In Higher set theory (Proc. Conf., Math. Forschungsinst., Oberwolfach, 1977) (Vol. 669, pp. 99–275). Springer. http://math.bu.edu/people/aki/e.pdf
73. Kanamori, A., Reinhardt, W. N., & Solovay, R. M. (1978). Strong axioms of infinity and elementary embeddings. http://math.bu.edu/people/aki/d.pdf
74. Kanamori, A., & Awerbuch-Friedlander, T. (1990). The compleat 0†. Mathematical Logic Quarterly, 36(2), 133–141. https://doi.org/10.1002/malq.19900360206
75. Kanamori, A. (2009). The higher infinite (Second, p. xxii+536). Springer-Verlag. https://link.springer.com/book/10.1007%2F978-3-540-88867-3
76. Kentaro, S. (2007). Double helix in large large cardinals and iteration of elementary embeddings. Annals of Pure and Applied Logic, 146(2-3), 199–236. https://doi.org/10.1016/j.apal.2007.02.003
77. Ketonen, J. (1974). Some combinatorial principles. Trans. Amer. Math. Soc., 188, 387–394. https://doi.org/10.1090/S0002-9947-1974-0332481-5
78. Koellner, P., & Woodin, W. H. (2010). Chapter 23: Large cardinals from Determinacy. Handbook of Set Theory. http://logic.harvard.edu/koellner/LCFD.pdf
79. Kunen, K. (1978). Saturated Ideals. J. Symbolic Logic, 43(1), 65–76. http://www.jstor.org/stable/2271949
80. Larson, P. B. (2013). A brief history of determinacy. http://www.users.miamioh.edu/larsonpb/determinacy_cabal.pdf
81. Laver, R. (1997). Implications between strong large cardinal axioms. Ann. Math. Logic, 90(1–3), 79–90.
82. Leshem, A. (2000). On the consistency of the definable tree property on \aleph_1. J. Symbolic Logic, 65(3), 1204–1214. https://doi.org/10.2307/2586696
83. Maddy, P. (1988). Believing the axioms. I. J. Symbolic Logic, 53(2), 181–511. https://doi.org/10.2307/2274520
84. Maddy, P. (1988). Believing the axioms. II. J. Symbolic Logic, 53(3), 736–764. https://doi.org/10.2307/2274569
85. Madore, D. (2017). A zoo of ordinals. http://www.madore.org/ david/math/ordinal-zoo.pdf
86. Makowsky, J. (1985). Vopěnkaś Principle and Compact Logics. J. Symbol Logic. https://www.jstor.org/stable/2273786?seq=1#page_scan_tab_contents
87. Mitchell, W. J. (1997). Jónsson Cardinals, Erdős Cardinals, and the Core Model. J. Symbol Logic.
88. Mitchell, W. J. (2001). The Covering Lemma. Handbook of Set Theory. http://www.math.cas.cz/ jech/library/mitchell/covering.ps
89. Miyamoto, T. (1998). A note on weak segments of PFA. Proceedings of the Sixth Asian Logic Conference, 175–197.
90. Nielsen, D. S., & Welch, P. (2018). Games and Ramsey-like cardinals.
91. Perlmutter, N. (2010). The large cardinals between supercompact and almost-huge. http://boolesrings.org/perlmutter/files/2013/07/HighJumpForJournal.pdf
92. Rathjen, M. (2006). The art of ordinal analysis. http://www.icm2006.org/proceedings/Vol_II/contents/ICM_Vol_2_03.pdf
93. Schanker, J. A. (2012). Partial near supercompactness. Ann. Pure Appl. Logic. https://doi.org/10.1016/j.apal.2012.08.001
94. Schanker, J. A. (2011). Weakly measurable cardinals. MLQ Math. Log. Q., 57(3), 266–280. https://doi.org/10.1002/malq.201010006
95. Schanker, J. A. (2011). Weakly measurable cardinals and partial near supercompactness [PhD thesis]. CUNY Graduate Center.
96. Schindler, R.-D. (2000). Proper forcing and remarkable cardinals. Bull. Symbolic Logic, 6(2), 176–184. https://doi.org/10.2307/421205
97. Sharpe, I., & Welch, P. (2011). Greatly Erdős cardinals with some generalizations to the Chang and Ramsey properties. Ann. Pure Appl. Logic, 162(11), 863–902. https://doi.org/10.1016/j.apal.2011.04.002
98. Shelah, S. (1994). Cardinal Arithmetic. Oxford Logic Guides, 29.
99. Silver, J. (1970). A large cardinal in the constructible universe. Fund. Math., 69, 93–100.
100. Silver, J. (1971). Some applications of model theory in set theory. Ann. Math. Logic, 3(1), 45–110.
101. Suzuki, A. (1998). Non-existence of generic elementary embeddings into the ground model. Tsukuba J. Math., 22(2), 343–347.
102. Suzuki, A. (1999). No elementary embedding from V into V is definable from parameters. J. Symbolic Logic, 64(4), 1591–1594. https://doi.org/10.2307/2586799
103. Trang, N., & Wilson, T. (2016). Determinacy from Strong Compactness of \omega_1.
104. Tryba, J. (1983). On Jónsson cardinals with uncountable cofinality. Israel Journal of Mathematics, 49(4).
105. Usuba, T. (2017). The downward directed grounds hypothesis and very large cardinals. Journal of Mathematical Logic, 17(02), 1750009. https://doi.org/10.1142/S021906131750009X
106. Usuba, T. (2019). Extendible cardinals and the mantle. Archive for Mathematical Logic, 58(1-2), 71–75. https://doi.org/10.1007/s00153-018-0625-4
107. Viale, M., & Weiß, C. (2011). On the consistency strength of the proper forcing axiom. Advances in Mathematics, 228(5), 2672–2687.
108. Villaveces, A. (1996). Chains of End Elementary Extensions of Models of Set Theory. JSTOR.
109. Welch, P. (1998). Some remarks on the maximality of Inner Models. Logic Colloquium. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.41.7037&rep=rep1&type=pdf
110. Welch, P. (2000). The Lengths of Infinite Time Turing Machine Computations. Bulletin of the London Mathematical Society, 32(2), 129–136.
111. Wilson, T. M. (2018). Weakly remarkable cardinals, Erdős cardinals, and the generic Vopěnka principle.
112. Woodin, W. H. (2010). Suitable extender models I. Journal of Mathematical Logic, 10(01n02), 101–339. https://doi.org/10.1142/S021906131000095X
113. Woodin, W. H. (2011). Suitable extender models II: beyond ω-huge. Journal of Mathematical Logic, 11(02), 115–436. https://doi.org/10.1142/S021906131100102X
114. Zapletal, J. (1996). A new proof of Kunenś inconsistency. Proc. Amer. Math. Soc., 124(7), 2203–2204. https://doi.org/10.1090/S0002-9939-96-03281-9

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