Chang’s Conjecture with \(\square _{\omega _1, 2}\) from an \(\omega _1\)-Erdős cardinal

1. Chang, C.C.: A note on the two cardinal problem. Proc. Am. Math. Soc. 16, 1148–1155 (1965)

   Article  MathSciNet  Google Scholar 

2. Cummings, J., Schimmerling, E.: Indexed squares. Isr. J. Math. 131, 61–99 (2002)

   Article  MathSciNet  Google Scholar 

3. Donder, D., Jensen, R.B., Koppelberg, B.J.: Some applications of the core model. In: Set Theory and Model Theory (Bonn, 1979), Volume 872 of Lecture Notes in Math., pp. 55–97. Springer, Berlin (1981)

4. Donder, H.-D., Levinski, J.-P.: Some principles related to Chang’s conjecture. Ann. Pure Appl. Logic 45(1), 39–101 (1989)

   Article  MathSciNet  Google Scholar 

5. Kanamori, A.: The Higher Infinite. Springer Monographs in Mathematics, 2nd ed. Springer, Berlin (2009). Large cardinals in set theory from their beginnings, Paperback reprint of the 2003 edition

6. Kanamori, A., Magidor, M.: The evolution of large cardinal axioms in set theory. In: Higher Set Theory (Proc. Conf., Math. Forschungsinst., Oberwolfach, 1977), Volume 669 of Lecture Notes in Math., pp. 99–275. Springer, Berlin (1978)

7. Sakai, H.: Chang’s conjecture and weak square. Arch. Math. Logic 52(1–2), 29–45 (2013)

   Article  MathSciNet  Google Scholar 

8. Schimmerling, E.: Combinatorial principles in the core model for one Woodin cardinal. Ann. Pure Appl. Logic 74(2), 153–201 (1995)

   Article  MathSciNet  Google Scholar 

9. Todorcevic, S.: Walks on ordinals and their characteristics. Progress in Mathematics, vol. 263. Birkhäuser Verlag, Basel (2007)

Download references