Second order logic

  1. Second order logic and foundations of mathematics, Bulletin of Symbolic Logic, Volume 7, Issue 4, December, 2001.

  2. Second order logic, set theory and foundations of mathematics. Epistemology versus Ontology, Essays of the Philosophy and Foundations of Mathematics in Honor of Per Martin-Löf, Editors: P. Dybjer, S. Lindström, E. Palmgren and G. Sundholm, Log. Epistemol. Unity Sci., 27, Springer, 2012, 371-380.

  3. Second order logic or set theory? Bulletin of Symbolic Logic, 18(1), 91-121, 2012.

  4. On second order characterizability, with Tapani Hyttinen and Kaisa Kangas. Logic Journal of the IGPL (2013) 21 (5): 767-787.

  5. Sort logic and foundations of mathematics, in: Infinity and Truth, Edited by: Chitat Chong, Qi Feng, Theodore A Slaman, W Hugh Woodin, Lecture Notes Series of the Institute for Mathematical Sciences, World Scientific, vol. 25, 2014, 171-186.

  6. An Ehrenfeucht-Fraisse Game for Lomega1omega, with Tong Wang. Mathematical Logic Quarterly 59, No 4-5, 357-370 (2013).

  7. Breaking the atom with Samson. In: Computation, Logic, Games, and Quantum Foundations. The Many Facets of Samson Abramsky. Essays Dedicated to Samson Abramsky on the Occasion of His 60th Birthday. Editors: Bob Coecke, Luke Ong, Prakash Panangaden, Lecture Notes in Computer Science, volume 7860, 2013, pp. 327-335.

  8. Internal Categoricity in Arithmetic and Set Theory, with Tong Wang. Notre Dame Journal of Formal Logic, 56:1(2015), 121-134.

  9. Boolean valued second order logic, with Daisuke Ikegami, Notre Dame Journal of Formal Logic, 56:1 (2015), 167-190.

  10. Categoricity and consistency in second order logic. Inquiry (An Interdisciplinary Journal of Philosophy), 58(1), 2015, 20-27.

  11. Second order logic and set theory. Philosophy Compass, 10 (2015), 463-478.


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