# The Cantor's attic library

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. Blass, Andreas. Chapter 6: Cardinal characteristics of the continuum. Handbook of Set Theory , 2010. www   bibtex
2. Cody, Brent and Gitman, Victoria. Easton's theorem for Ramsey and strongly Ramsey cardinals. (In preparation) bibtex
3. Corazza, Paul. The Wholeness Axiom and Laver sequences. Annals of Pure and Applied Logic pp. 157--260, October, 2000. bibtex
4. Corazza, Paul. The gap between ${\rm I}_3$ and the wholeness axiom. Fund Math 179(1):43--60, 2003. www   DOI   MR   bibtex
5. 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
6. Gitman, Victoria. Ramsey-like cardinals. The Journal of Symbolic Logic 76(2):519-540, 2011. www   arχiv   MR   bibtex
7. Gitman, Victoria and Johnstone, Thomas. Indestructibility for Ramsey and Ramsey-like cardinals. (In preparation) bibtex
8. Hamkins, Joel David and Lewis, Andy. Infinite time Turing machines. J Symbolic Logic 65(2):567--604, 2000. www   arχiv   DOI   MR   bibtex
9. Hamkins, Joel David. Infinite time Turing machines. Minds and Machines 12(4):521--539, 2002. (special issue devoted to hypercomputation) www   arχiv   bibtex
10. 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
11. Hamkins, Joel David. The wholeness axioms and V=HOD. Arch Math Logic 40(1):1--8, 2001. www   arχiv   DOI   MR   bibtex
12. Hamkins, Joel David. Tall cardinals. MLQ Math Log Q 55(1):68--86, 2009. www   DOI   MR   bibtex
13. bibtext=@ARTICLE{HamkinsKirmayerPerlmutter:GeneralizationsOfKunenInconsistency, AUTHOR = {Hamkins, Joel David and Kirmayer, Greg and Perlmutter, Norman}, TITLE = {Generalizations of the {K}unen inconsistency}, JOURNAL = {}, YEAR = {}, volume = {}, number = {}, pages = {}, month = {}, note = {submitted}, url = {http://arxiv.org/abs/1106.1951}, eprint = {1106.1951}, abstract = {}, keywords = {}, source = {},}
14. Jech, Thomas J. Set Theory. Third, Springer, Berlin, 2003. bibtex
15. Kanamori, Akihiro. The higher infinite. Second, Springer-Verlag, Berlin, 2009. (Large cardinals in set theory from their beginnings, Paperback reprint of the 2003 edition) bibtex
16. Kunen, Kenneth. Saturated Ideals. J Symbolic Logic 43(1):65--76, 1978. www   bibtex
17. Schanker, Jason A. Weakly measurable cardinals. MLQ Math Log Q 57(3):266--280, 2011. www   DOI   bibtex
18. [G] bibtex=@article {Suzuki1998:NojVtoVinV[G], AUTHOR = {Suzuki, Akira}, TITLE = {Non-existence of generic elementary embeddings into the ground model}, JOURNAL = {Tsukuba J. Math.}, FJOURNAL = {Tsukuba Journal of Mathematics}, VOLUME = {22}, YEAR = {1998}, NUMBER = {2}, PAGES = {343--347}, ISSN = {0387-4982}, MRCLASS = {03E55 (03E05)}, MRNUMBER = {MR1650737 (2000a:03087)}, Abstract = {The author proves that if $j\colon V\rightarrow M$ is an elementary embedding defined in a set generic extension of $V$, then $V \not \subseteq M$. The proof generalizes Woodin's proof of Kunen's theorem to generic embeddings. }MRREVIEWER = {Douglas R. Burke},}
19. 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
20. Welch, Philip. The Lengths of Infinite Time Turing Machine Computations. Bulletin of the London Mathematical Society 32(2):129--136, 2000. bibtex
21. Welch, Philip. Eventually Infinite Time Turing Machine Degrees: Infinite Time Decidable reals. Journal of Symbolic Logic 65(3):1193--1203, 2000. bibtex
22. Zapletal, Jind{\v{r}}ich. 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.