1.
Slow
P-point Ultrafilters, pdf-file,
submitted
2.
Abstract density and ideal of sets, (joint with Mauro Di Nasso), arXiv, Acta Arithmetica, to appear.
3.
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.
4. 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.
5.
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.
6.
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
7.
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
8. Detailed Structure for Freiman’s 3k-3 Theorem, pdf-file, INTEGERS: The Electronic Journal of Combinatorial Number Theory, 15A (2015), A9.
9.
Detailed Structure for The Sum of Two
Distinct Sets, pdf-file
10. 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.
11. 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).
12. Plunnecke’s Theorem for asymptotic
densities, pdf-file,
The Transactions of American Mathematical Society, Vol. 363 (2011),
5059 --- 5070.
13. 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.
14. Freiman’s 3k-3+b Conjecture for Almost
Bi-arithmetic Progression, pdf-file.
15. 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.
16. 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.
17. 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).
18. 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.
19. 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.
20. 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.
21. 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.
22. 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.
23. Inverse
Problem For Upper Asymptotic Density, pdf-file, The Transactions of
American Mathematical Society, Vol. 355 (2003), No. 1, pp. 57 --- 78.
24. 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.
25. Nonstandard
Methods For Upper Banach Density Problems, pdf-file, the
Journal of Number Theory, 91 (2001), pp. 20---38.
26. Sumset Phenomenon, pdf-file, The
Proceedings of American Mathematical Society, Vol. 130, No.3 (2002),
pp.855---861.
27. Maharam Type of a Loeb Space,
(with H. Jerome Keisler), pdf-file, The Journal of Symbolic Logic,
65, No. 2 (2000), pp. 550---566..
28. Distinguishing
Three Saturation Properties in Nonstandard Analysis, pdf-file, Annals of Pure and Applied
Logic, 98 (1999), pp. 157---171.
29. Existence
of Some Sparse Sets of Nonstandard Natural Numbers, pdf-file,
The Journal of Symbolic Logic, 66, No. 2 (2001), pp. 959---973.
30. Possible
Size of an Ultrapower of $\omega$, (with Saharon Shelah), pdf-file,
Archive for the Mathematical Logic, 38 (1999), pp. 61---77.
31. The
Compactness of Loeb Spaces, (with Saharon Shelah), pdf-file, The Journal of Symbolic Logic,
63 (1998), No. 4, pp. 1371---1392.
32. Type
Two Cuts, Bad Cuts and Very Bad Cuts, pdf-file, The Journal of Symbolic Logic,
62 (1997), No. 4, pp. 1241---1252.
33. Can
a Small Forcing Create Kurepa Trees? pdf-file,
(with Saharon Shelah),
Annals of Pure And Applied Logic, 85 (1997), pp. 47---68.
34. Essential
Kurepa Trees Versus Essential Jech--Kunen Trees, pdf-file, (with Saharon
Shelah), Annals of Pure And Applied Logic, 69 (1994),
pp. 107---131.
35. The
Strength Of The Isomorphism Property, pdf-file, (with Saharon
Shelah), The Journal of Symbolic Logic, 59 (1994),
No. 1, pp. 292---301.
36. The
Differences Between Kurepa Trees And Jech--Kunen Trees, pdf-file,
Archive for the Mathematical Logic, 32 (1993), pp. 369---379.
37. Game
Sentences And Ultrapowers,
(with H. Jerome Keisler), Annals of Pure And Applied Logic, 60 (1993), pp.
261---274.
38. 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.
39. 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.
40. A
Theorem On The Isomorphism Property, pdf-file,
The Journal of Symbolic Logic, 57, No 3 (1992), pp. 1011---1017.
41. A
Model In Which Every Kurepa Tree Is Thick, pdf-file, Notre
Dame Journal of Formal Logic, 33, No 1 (1992), pp. 120---125.
42. The
Isomorphism Property Versus The Special Model Axiom , pdf-file,
The Journal of Symbolic Logic, 57, No 3 (1992), pp. 975---987.
43. U-Monad
Topologies of Hyperfinite Time Lines, pdf-file, The Journal of Symbolic Logic, 57, No
2 (1992), pp. 534---539.
44. U-Lusin Sets In Hyperfinite Time
Lines, pdf-file,
The Journal of Symbolic Logic, 57, No 2 (1992), pp. 528---533.
45. Cuts
In Hyperfinite Time Lines, pdf-file, The Journal of Symbolic Logic,
57, No 2 (1992), pp. 522---527.
46. Some
Independence Results Related To Kurepa Tree, pdf-file, Notre
Dame Journal of Formal Logic, 32, No. 3 (1991), pp. 448---457.
Expository
articles:
47. Nonstandard
Analysis and Its Applications (in Chinese), Scientia
Sinica Mathematica A, 2016, 46: 371–408, link
48. 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
49. 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
50. 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
51. 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
52. Applications
of Nonstandard Analysis in Additive Number Theory, pdf-file, The Bulletin of Symbolic Logic, 6, No.
3 (2000), pp. 331---341.
53. 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.