Some Second Order Set Theory

  • Joel David Hamkins
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5378)


This article surveys two recent developments in set theory sharing an essential second-order nature, namely, the modal logic of forcing, oriented upward from the universe of set theory to its forcing extensions; and set-theoretic geology, oriented downward from the universe to the inner models over which it arises by forcing. The research is a mixture of ideas from several parts of logic, including, of course, set theory and forcing, but also modal logic, finite combinatorics and the philosophy of mathematics, for it invites a mathematical engagement with various philosophical views on the nature of mathematical existence.


Maximality Principle Modal Logic Ground Model Kripke Model Force Extension 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Joel David Hamkins
    • 1
  1. 1.The City University of New York, The Graduate Center of CUNY, Mathematics, 365 Fifth Avenue, New York, NY 10016 and The College of Staten Island of CUNY, MathematicsStaten Island

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