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Some Second Order Set Theory

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

Abstract

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.

Keywords

Maximality Principle Modal Logic Ground Model Kripke Model Force Extension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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