Renling Jin's Publication List:

Research articles:

  1. Approximate polynomial structure in additively large sets, (joint with Mauro Di Nasso, Isaac Goldbring, Steven Leth, Martino Lupini, Karl Mahlburg), arXiv, INTEGERS: The Electronic Journal of Combinatorial Number Theory, 16 (2016), A49.
  2. High density piecewise syndeticity of product sets in amenable groups, (joint with Mauro Di Nasso, Isaac Goldbring, Steven Leth, Martino Lupini, Karl Mahlburg), arXiv, The Journal of Symbolic Logic, Vol. 81 (2016), Issue 4, 1555 --- 1562.
  3. A monad measure space for logarithmic density, (joint with Mauro Di Nasso, Isaac Goldbring, Steven Leth, Martino Lupini, Karl Mahlburg), arXiv, Monatshefte für Mathematik, 181 (2016), no. 3, 577 --- 599.
  4. High Density Piecewise Syndeticity of Sumsets, (joint with Mauro Di Nasso, Isaac Goldbring, Steven Leth, Martino Lupini, Karl Mahlburg), Advances in Mathematics, 278 (2015) 1 --- 33, arXiv
  5. Progress on a Sumset Conjecture of Erdos, (joint with Mauro Di Nasso, Isaac Goldbring, Steven Leth, Martino Lupini, Karl Mahlburg), arXiv, Canadian Journal of Mathematics, 67 (2015), 795 --- 809
  6. Detailed Structure for Freiman’s 3k-3 Theorem, pdf-file, INTEGERS: The Electronic Journal of Combinatorial Number Theory, 15A (2015), A9.
  7. Detailed Structure for The Sum of Two Distinct Sets, pdf-file
  8. An Integer Construction of Infinitesimals, (with A. Borovik and M. G. Katz) Notre Dame Journal of Formal Logic, Vol. 53, No. 4 (2012), 557 --- 570.
  9. Density version of Plunnecke inequality – Epsilon-Delta Approach, pdf-file, Combinatorial and Additive Number Theory, CANT 2011-2012, Springer Proceedings in Mathematics and Statistics, Vol. 101, M. Natheanson edited (2014).
  10. Plunnecke’s Theorem for asymptotic densities, pdf-file, The Transactions of American Mathematical Society, Vol. 363 (2011), 5059 --- 5070.
  11. Finding integral diagonal pairs in a two dimensional N-set (joint with Lev A. Borisov), pdf-file, The Proceedings of American Mathematical Society, Vol. 139 (2011), pp 2431 --- 2434.
  12. Freiman’s 3k-3+b Conjecture for Almost Bi-arithmetic Progression, pdf-file.
  13. Characterizing the structure of A+B when A+B has small upper Banach density, pdf-file, The Journal of Number Theory, Vol. 130, No. 8  (2010), pp 1785 --- 1800.
  14. Inverse Problems For Cuts, pdf-file (Springer-Verlag/Wien is given as the copyrigt owner), Logic and Analysis, vol. 1, No. 1 (2007), pp 61 --- 89.
  15. Freiman’s Inverse Problem with Small Doubling Property (short version 47 pages: link), Advances in Mathematics, Vol 216, No. 2, (2007), pp 711-752. (long version 72 pages: pdf-file).
  16. Kneser’s Theorem for Upper Banach Density, (with Prerna Bihani), pdf-file, vol 18, no 2 (2006) of Journal de theorie des nombres de Bordeaux, 323 --- 343.
  17. Solution to the Inverse Problem for Upper Asymptotic Density, pdf-file, Journal für die reine und angewandte Mathematik (Crelle's Journal), 595 (2006), pp.121 --- 166.
  18. On Some Questions of Hrbacek and Di Nasso, pdf-file, Nonstandard Models of Arithmetic and Set Theory (edited by Ali Enayat and Roman Kossak), Contemporary Mathematics, volume 361, American Mathematical Society, 2004.
  19. Inverse Problem For Upper Asymptotic Density II, pdf-file, in Nonstandard Methods and Applications in Mathematics, edited by N. J. Cutland, M. Di Nasso, and D. A. Ross, Lecture Notes in Logic 25, published by A. K. Peters 2006.
  20. Abelian Groups with Layered Tiles and Sumset Phenomenon, (with H. Jerome Keisler), pdf-file, The Transactions of American Mathematical Society, Vol. 355 (2003), No. 1, pp. 79 ---97.
  21. Inverse Problem For Upper Asymptotic Density, pdf-file, The Transactions of American Mathematical Society, Vol. 355 (2003), No. 1, pp. 57 --- 78.
  22. Standardizing Nonstandard Methods For Upper Banach Density Problems, pdf-file, in DIMACS Series, Unusual Applications of Number Theory, edited by Melvyn Nathanson, vol. 64, 2004, pp. 109 --- 124.
  23. Nonstandard Methods For Upper Banach Density Problems, pdf-file, the Journal of Number Theory, 91 (2001), pp. 20---38.
  24. Sumset Phenomenon, pdf-file, The Proceedings of American Mathematical Society, Vol. 130, No.3 (2002), pp.855---861.
  25. Maharam Type of a Loeb Space, (with H. Jerome Keisler), pdf-file, The Journal of Symbolic Logic, 65, No. 2 (2000), pp. 550---566..
  26. Distinguishing Three Saturation Properties in Nonstandard Analysis, pdf-file, Annals of Pure and Applied Logic, 98 (1999), pp. 157---171.
  27. Existence of Some Sparse Sets of Nonstandard Natural Numbers, pdf-file, The Journal of Symbolic Logic, 66, No. 2 (2001), pp. 959---973.
  28. Possible Size of an Ultrapower of $\omega$, (with Saharon Shelah), pdf-file, Archive for the Mathematical Logic, 38 (1999), pp. 61---77.
  29. The Compactness of Loeb Spaces, (with Saharon Shelah), pdf-file, The Journal of Symbolic Logic, 63 (1998), No. 4, pp. 1371---1392.
  30. Type Two Cuts, Bad Cuts and Very Bad Cuts, pdf-file, The Journal of Symbolic Logic, 62 (1997), No. 4, pp. 1241---1252.
  31. Can a Small Forcing Create Kurepa Trees? pdf-file, (with Saharon Shelah), Annals of Pure And Applied Logic, 85 (1997), pp. 47---68.
  32. Essential Kurepa Trees Versus Essential Jech--Kunen Trees, pdf-file, (with Saharon Shelah), Annals of Pure And Applied Logic, 69 (1994), pp. 107---131.
  33. The Strength Of The Isomorphism Property, pdf-file, (with Saharon Shelah), The Journal of Symbolic Logic, 59 (1994), No. 1, pp. 292---301.
  34. The Differences Between Kurepa Trees And Jech--Kunen Trees, pdf-file, Archive for the Mathematical Logic, 32 (1993), pp. 369---379.
  35. Game Sentences And Ultrapowers, (with H. Jerome Keisler), Annals of Pure And Applied Logic, 60 (1993), pp. 261---274.
  36. Planting Kurepa Trees And Killing Jech--Kunen Trees By Using One Inaccessible Cardinal, pdf-file, (with Saharon Shelah), Fundamenta Mathematicae, 141 (1992), pp. 287---296.
  37. A Model In Which There Are Jech--Kunen Trees But There Are No Kurepa Trees, pdf-file, (with Saharon Shelah), Israel Journal of Mathematics, 84 (1993), pp. 1---16.
  38. A Theorem On The Isomorphism Property, pdf-file, The Journal of Symbolic Logic, 57, No 3 (1992), pp. 1011---1017.
  39. A Model In Which Every Kurepa Tree Is Thick, pdf-file, Notre Dame Journal of Formal Logic, 33, No 1 (1992), pp. 120---125.
  40. The Isomorphism Property Versus The Special Model Axiom , pdf-file, The Journal of Symbolic Logic, 57, No 3 (1992), pp. 975---987.
  41. U-Monad Topologies of Hyperfinite Time Lines, pdf-file, The Journal of Symbolic Logic, 57, No 2 (1992), pp. 534---539.
  42. U-Lusin Sets In Hyperfinite Time Lines, pdf-file, The Journal of Symbolic Logic, 57, No 2 (1992), pp. 528---533.
  43. Cuts In Hyperfinite Time Lines, pdf-file, The Journal of Symbolic Logic, 57, No 2 (1992), pp. 522---527.
  44. Some Independence Results Related To Kurepa Tree, pdf-file, Notre Dame Journal of Formal Logic, 32, No. 3 (1991), pp. 448---457.

 

Expository articles:

  1. Nonstandard Analysis and Its Applications (in Chinese), Scientia Sinica Mathematica A, 2016, 46: 371–408, link
  2. Density Problems and Freiman’s Inverse Problems, Chapter 10 in Nonstandard Analysis for Working Mathematician-Second Edition, edited by Peter A. Loeb and Manfred, P. H. Wolff, Springer, 2015
  3. Ultrapower of N and Density Problems, pdf-file, Proceedings of Workshop “UltraMath 2008-Applications of Ultrafilters and Ultraproducts in Mathematics”, edited by Mauro Di Nasso, Vitaly Bergelson, Andreas Blass, Renling Jin, Pisa, Italy, 2008
  4. Introduction of Nonstandard Methods for Number Theorists, Proceedings of the CANT (2005) Conference in Honor of Mel Nathanson, INTEGERS: The Electronic Journal of Combinatorial Number Theory, vol. 8, no. 2, (2008), A7
  5. Nonstandard Methods for Additive and Combinatorial Number Theory—A Survey, pdf-file, in The Strength of Nonstandard Analysis, ed. by Imme van den Berg and Vitor Neves, Springer Publisher, January 2007
  6. Applications of Nonstandard Analysis in Additive Number Theory, pdf-file, The Bulletin of Symbolic Logic, 6, No. 3 (2000), pp. 331---341.
  7. Better nonstandard universes with applications, pdf-file, in Nonstandard Analysis: Theory and Applications, ed. by N. J. Cutland, C. W. Henson, and L. Arkeryd, Kluwer Publishers 1997.