- 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.
`@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}, ADDRESS = {Berlin}, YEAR = {2009}, MRCLASS = {03E35 (03B45 03E40)}, MRNUMBER = {2540935 (2011a:03053)}, DOI = {10.1007/978-3-540-92701-3_3}, URL = {http://dx.doi.org/10.1007/978-3-540-92701-3_3}, }`

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.

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.