Some second order set theory

  • J. D. Hamkins, “Some second order set theory,” in Logic and its applications, R.~Ramanujam and S.~Sarukkai, Eds., Berlin: Springer, 2009, vol. 5378, pp. 36-50.  
    AUTHOR = {Hamkins, Joel David},
    TITLE = {Some second order set theory},
    BOOKTITLE = {Logic and its applications},
    SERIES = {Lecture Notes in Comput.~Sci.},
    VOLUME = {5378},
    PAGES = {36--50},
    PUBLISHER = {Springer},
    EDITOR = {R.~Ramanujam and S.~Sarukkai},
    ADDRESS = {Berlin},
    YEAR = {2009},
    MRCLASS = {03E35 (03B45 03E40)},
    MRNUMBER = {2540935 (2011a:03053)},
    DOI = {10.1007/978-3-540-92701-3_3},
    URL = {},

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.

One thought on “Some second order set theory

  1. Hi,
    I am a researcher in logic from Chennai Mathematical Institute, Chennai, India. Could you please send me the paper titled “Some second order set theory”?


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