Moving Up and Down in the Generic Multiverse

1. Esakia, L., Löwe, B.: Fatal Heyting algebras and forcing persistent sentences. Studia Logica 100(1-2), 163–173 (2012)

   Article  MathSciNet  MATH  Google Scholar 

2. Friedman, S., Fuchino, S., Sakai, H.: On the set-generic multiverse (submitted, 2012)

   Google Scholar 

3. Fuchs, G.: Closed maximality principles: implications, separations and combinations. Journal of Symbolic Logic 73(1), 276–308 (2008)

   Article  MathSciNet  MATH  Google Scholar 

4. Fuchs, G.: Combined maximality principles up to large cardinals. Journal of Symbolic Logic 74(3), 1015–1046 (2009)

   Article  MathSciNet  MATH  Google Scholar 

5. Fuchs, G., Hamkins, J.D., Reitz, J.: Set-theoretic geology (submitted, 2011)

   Google Scholar 

6. Hamkins, J.D.: A simple maximality principle. Journal of Symbolic Logic 68(2), 527–550 (2003)

   Article  MathSciNet  MATH  Google Scholar 

7. Hamkins, J.D.: The Ground Axiom. Oberwolfach Reports 2(4), 3160–3162 (2005)

   Google Scholar 

8. Hamkins, J.D.: Some Second Order Set Theory. In: Ramanujam, R., Sarukkai, S. (eds.) ICLA 2009. LNCS (LNAI), vol. 5378, pp. 36–50. Springer, Heidelberg (2009)

   Chapter  Google Scholar 

9. Hamkins, J.D.: The set-theoretic multiverse. Review of Symbolic Logic 5, 416–449 (2012), doi:10.1017/S1755020311000359

   Article  MATH  Google Scholar 

10. Hamkins, J.D., Leibman, G., Löwe, B.: Structural connections between a forcing class and its modal logic (submitted, 2012)

    Google Scholar 

11. Hamkins, J.D., Löwe, B.: The modal logic of forcing. Transactions of the American Mathematical Society 360(4), 1793–1817 (2008)

    Article  MathSciNet  MATH  Google Scholar 

12. Hamkins, J.D., Woodin, W.H.: The necessary maximality principle for c.c.c. forcing is equiconsistent with a weakly compact cardinal. Mathematical Logic Quarterly 51(5), 493–498 (2005)

    Article  MathSciNet  MATH  Google Scholar 

13. Jech, T.: Set Theory, 3rd edn. Springer Monographs in Mathematics. Springer, Heidelberg (2003)

    MATH  Google Scholar 

14. Laver, R.: Certain very large cardinals are not created in small forcing extensions. Annals of Pure and Applied Logic 149(1-3), 1–6 (2007)

    Article  MathSciNet  MATH  Google Scholar 

15. Leibman, G.: Consistency strengths of modified maximality principles. PhD thesis, City University of New York (2004)

    Google Scholar 

16. Leibman, G.: The consistency strength of \({\rm MP}_{\rm CCC}(\Bbb R)\). Notre Dame Journal of Formal Logic 51(2), 181–193 (2010)

    Article  MathSciNet  MATH  Google Scholar 

17. Reitz, J.: The Ground Axiom. PhD thesis, City University of New York (September 2006)

    Google Scholar 

18. Reitz, J.: The Ground Axiom. Journal of Symbolic Logic 72(4), 1299–1317 (2007)

    Article  MathSciNet  MATH  Google Scholar 

19. Rittberg, C.J.: The modal logic of forcing. Master’s thesis, Westfälische Wilhelms-Universität Münster (2010)

    Google Scholar 

20. van Benthem, J.F.A.K.: The logic of time. A model-theoretic investigation into the varieties of temporal ontology and temporal discourse. Synthese Library, vol. 156. D. Reidel Publishing Co., Dordrecht (1983)

    MATH  Google Scholar 

21. Woodin, W.H.: The continuum hypothesis, the generic multiverse of sets, and the ω conjecture (2009) (preprint)

    Google Scholar 

Download references