1
Combinatorial Proof of Szemeredi's Theorem
in Nonstandard Analysisy, pdf-file
2
Rapid Interval P-point, (joint with Jialiang He and Shuguo Zhang), pdf-file, Topology and Its
Applications, Volume 283, 1 September 2020, 107333
3
Slow P-point Ultrafilters, pdf-file, Journal of Symbolic Logic, 85, Issue 1, (2020), 26 --- 36.
4
Abstract density and ideal of sets, (joint with Mauro Di Nasso), pdf-file, Acta Arithmetica, 185(4), 301 --- 313, 2018.
5
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.
6 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.
7
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.
8
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
9
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
10 Detailed Structure for Freiman’s 3k-3 Theorem, pdf-file, INTEGERS: The Electronic Journal of Combinatorial Number Theory, 15A (2015), A9.
11
Detailed Structure for The Sum of Two
Distinct Sets, pdf-file
12
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.
13
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).
14
Plunnecke’s
Theorem for asymptotic densities, pdf-file, The Transactions of American
Mathematical Society, Vol. 363 (2011), 5059 --- 5070.
15
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.
16
Freiman’s
3k-3+b Conjecture for Almost Bi-arithmetic Progression, pdf-file.
17
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.
18
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.
19
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).
20
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.
21
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.
22
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.
23
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.
24
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.
25
Inverse Problem For Upper Asymptotic
Density, pdf-file,
The Transactions of American Mathematical Society, Vol. 355 (2003), No. 1, pp.
57 --- 78.
26
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.
27
Nonstandard Methods For Upper Banach Density Problems, pdf-file, the Journal of Number Theory, 91
(2001), pp. 20---38.
28
Sumset
Phenomenon, pdf-file,
The Proceedings of American Mathematical Society, Vol. 130, No.3 (2002),
pp.855---861.
29
Maharam
Type of a Loeb Space, (with H. Jerome Keisler),
pdf-file,
The Journal of Symbolic Logic, 65, No. 2 (2000), pp. 550---566..
30
Distinguishing Three Saturation Properties
in Nonstandard Analysis, pdf-file,
Annals of Pure and Applied Logic, 98 (1999), pp. 157---171.
31
Existence of Some Sparse Sets of
Nonstandard Natural Numbers, pdf-file, The Journal of Symbolic Logic,
66, No. 2 (2001), pp. 959---973.
32
Possible Size of an Ultrapower
of $\omega$, (with Saharon Shelah), pdf-file, Archive for the Mathematical
Logic, 38 (1999), pp. 61---77.
33
The Compactness of Loeb Spaces,
(with Saharon Shelah), pdf-file,
The Journal of Symbolic Logic, 63 (1998), No. 4, pp. 1371---1392.
34
Type Two Cuts, Bad Cuts and Very Bad Cuts,
pdf-file, The
Journal of Symbolic Logic, 62 (1997), No. 4, pp. 1241---1252.
35
Can a Small Forcing Create Kurepa Trees? pdf-file,
(with Saharon Shelah),
Annals of Pure And Applied Logic, 85 (1997), pp. 47---68.
36
Essential Kurepa
Trees Versus Essential Jech--Kunen
Trees, pdf-file,
(with Saharon Shelah),
Annals of Pure And Applied Logic, 69 (1994), pp. 107---131.
37
The Strength Of The Isomorphism Property, pdf-file,
(with Saharon Shelah), The
Journal of Symbolic Logic, 59 (1994), No. 1, pp. 292---301.
38
The Differences Between Kurepa Trees And Jech--Kunen Trees, pdf-file, Archive for the Mathematical
Logic, 32 (1993), pp. 369---379.
39
Game Sentences And
Ultrapowers, (with H. Jerome Keisler), Annals
of Pure And Applied Logic, 60 (1993), pp. 261---274.
40
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.
41
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.
42
A Theorem On The Isomorphism Property,
pdf-file, The Journal of Symbolic
Logic, 57, No 3 (1992), pp. 1011---1017.
43
A Model In Which Every Kurepa
Tree Is Thick, pdf-file,
Notre Dame Journal of Formal Logic, 33, No 1 (1992), pp. 120---125.
44
The Isomorphism Property Versus The
Special Model Axiom , pdf-file, The
Journal of Symbolic Logic, 57, No 3 (1992), pp. 975---987.
45
U-Monad Topologies of Hyperfinite
Time Lines, pdf-file, The
Journal of Symbolic Logic, 57, No 2 (1992), pp. 534---539.
46
U-Lusin Sets In Hyperfinite Time Lines, pdf-file, The Journal of Symbolic Logic,
57, No 2 (1992), pp. 528---533.
47
Cuts In Hyperfinite
Time Lines, pdf-file,
The Journal of Symbolic Logic, 57, No 2 (1992), pp. 522---527.
48
Some Independence Results Related To Kurepa Tree, pdf-file, Notre Dame Journal of Formal
Logic, 32, No. 3 (1991), pp. 448---457.
Expository
articles:
49
Nonstandard Analysis and Its Applications
(in Chinese), Scientia Sinica
Mathematica A, 2016, 46: 371–408, link
50
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
51
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
52
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
53
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
54
Applications of Nonstandard Analysis in
Additive Number Theory, pdf-file,
The Bulletin of Symbolic Logic, 6, No. 3 (2000), pp. 331---341.
55
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.