Moving Up and Down in the Generic Multiverse

  • Joel David Hamkins
  • Benedikt Löwe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7750)


We investigate the modal logic of the generic multiverse which is a bimodal logic with operators corresponding to the relations “is a forcing extension of” and “is a ground model of”. The fragment of the first relation is the modal logic of forcing and was studied by the authors in earlier work. The fragment of the second relation is the modal logic of grounds and will be studied here for the first time. In addition, we discuss which combinations of modal logics are possible for the two fragments.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Joel David Hamkins
    • 1
    • 2
  • Benedikt Löwe
    • 3
    • 4
  1. 1.Mathematics ProgramThe Graduate Center of the City University of New YorkNew YorkUnited States of America
  2. 2.Department of MathematicsCollege of Staten Island of CUNYStaten IslandUnited States of America
  3. 3.Institute for Logic, Language and ComputationUniversiteit van AmsterdamAmsterdamThe Netherlands
  4. 4.Department MathematikUniversität HamburgHamburgGermany

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