# Some second order set theory

• J. D. Hamkins, “Some second order set theory,” in Logic and its applications, R.~Ramanujam and S.~Sarukkai, Eds., Springer, 2009, vol. 5378, pp. 36-50.
@INCOLLECTION{Hamkins2009:SomeSecondOrderSetTheory,
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},
YEAR = {2009},
MRCLASS = {03E35 (03B45 03E40)},
MRNUMBER = {2540935 (2011a:03053)},
DOI = {10.1007/978-3-540-92701-3_3},
URL = {http://wp.me/p5M0LV-3E},
}

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”?

Vinod.