Renling Jin's
Publication List:
Research
articles:
1. A
Simple Combinatorial Proof of Szemeredi’s Theorem via
Three Levels of Infinities, pdf-file,
Discrete Analysis, September 25, 2023.
2. Generic
Existence of Interval P-point, (joint with Jialiang
He and Shuguo Zhang), pdf-file,
Archive for Mathematical Logic, 07 November, 2022
- Rapid
Interval P-point, (joint with Jialiang
He and Shuguo Zhang), pdf-file,
Topology and Its Applications, Volume 283, 1 September 2020, 107333
- Slow
P-point Ultrafilters, pdf-file, Journal of Symbolic Logic, 85, Issue
1, (2020), 26 --- 36.
- Abstract
density and ideal of sets, (joint with Mauro Di Nasso), pdf-file, Acta Arithmetica, 185(4), 301 --- 313, 2018.
- 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.
- 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.
- A monad measure space for logarithmic density, (joint with Mauro Di Nasso, Isaac Goldbring,
Steven Leth, Martino Lupini, Karl Mahlburg), arXiv, Monatshefte
fur Mathematik, 181 (2016), no. 3, 577 --- 599.
- 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
- 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
- Detailed
Structure for Freiman’s 3k-3 Theorem, pdf-file, INTEGERS: The Electronic
Journal of Combinatorial Number Theory, 15A (2015), A9.
- Detailed Structure for The Sum of Two Distinct
Sets, pdf-file
- 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.
- 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).
- Plunnecke’s Theorem for asymptotic densities, pdf-file, The Transactions of
American Mathematical Society, Vol. 363 (2011), 5059 --- 5070.
- 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.
- Freiman’s 3k-3+b Conjecture for Almost
Bi-arithmetic Progression, pdf-file.
- 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.
- 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.
- 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).
- 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.
- Solution to the Inverse Problem for Upper
Asymptotic Density, pdf-file, Journal fur die reine und angewandte Mathematik (Crelle's Journal), 595 (2006), pp.121 --- 166.
- 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.
- 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.
- 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.
- Inverse Problem For Upper
Asymptotic Density, pdf-file, The Transactions of American Mathematical
Society, Vol. 355 (2003), No. 1, pp. 57 --- 78.
- 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.
- Nonstandard Methods For
Upper Banach Density Problems,
pdf-file,
the Journal of Number Theory, 91 (2001), pp. 20---38.
- Sumset Phenomenon, pdf-file,
The Proceedings of American Mathematical Society, Vol. 130, No.3 (2002),
pp.855---861.
- Maharam Type of a Loeb Space, (with H. Jerome Keisler), pdf-file, The Journal of Symbolic
Logic, 65, No. 2 (2000), pp. 550---566..
- Distinguishing Three Saturation Properties in
Nonstandard Analysis,
pdf-file,
Annals of Pure and Applied Logic, 98 (1999), pp. 157---171.
- Existence of Some Sparse Sets of Nonstandard
Natural Numbers, pdf-file,
The Journal of Symbolic Logic, 66, No. 2 (2001), pp. 959---973.
- Possible Size of an Ultrapower
of $\omega$, (with Saharon Shelah), pdf-file, Archive for the
Mathematical Logic, 38 (1999), pp. 61---77.
- The Compactness of Loeb Spaces, (with Saharon Shelah),
pdf-file,
The Journal of Symbolic Logic, 63 (1998), No. 4, pp. 1371---1392.
- Type Two Cuts, Bad Cuts and Very Bad Cuts, pdf-file, The Journal of Symbolic Logic, 62
(1997), No. 4, pp. 1241---1252.
- Can a Small Forcing Create Kurepa
Trees? pdf-file,
(with Saharon Shelah), Annals of Pure And Applied Logic, 85 (1997), pp. 47---68.
- Essential Kurepa Trees
Versus Essential Jech--Kunen Trees, pdf-file, (with Saharon
Shelah), Annals of Pure And Applied Logic, 69
(1994), pp. 107---131.
- The Strength Of The
Isomorphism Property, pdf-file,
(with Saharon Shelah), The Journal of Symbolic
Logic, 59 (1994), No. 1, pp. 292---301.
- The Differences Between Kurepa
Trees And Jech--Kunen
Trees, pdf-file, Archive for the
Mathematical Logic, 32 (1993), pp. 369---379.
- Game Sentences And Ultrapowers,
(with H. Jerome Keisler), Annals of Pure And Applied Logic, 60 (1993), pp.
261---274.
- 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.
- 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.
- A Theorem On The
Isomorphism Property, pdf-file, The Journal of
Symbolic Logic, 57, No 3 (1992), pp. 1011---1017.
- A Model In Which Every Kurepa Tree Is Thick, pdf-file,
Notre Dame Journal of Formal Logic, 33, No 1 (1992), pp. 120---125.
- The Isomorphism Property Versus The Special Model
Axiom , pdf-file, The Journal of Symbolic Logic, 57, No 3 (1992),
pp. 975---987.
- U-Monad Topologies of Hyperfinite Time Lines,
pdf-file, The Journal of
Symbolic Logic, 57, No 2 (1992), pp. 534---539.
- U-Lusin Sets In Hyperfinite Time Lines, pdf-file,
The Journal of Symbolic Logic, 57, No 2 (1992), pp. 528---533.
- Cuts In Hyperfinite Time Lines, pdf-file,
The Journal of Symbolic Logic, 57, No 2 (1992), pp. 522---527.
- Some Independence Results Related To Kurepa Tree, pdf-file,
Notre Dame Journal of Formal Logic, 32, No. 3 (1991), pp. 448---457.
- 紧性与全聚点关系的推广,上海师范大学学报(自然科学版),1984(3)
51. Expository articles:
- Nonstandard Analysis and Its Applications (in Chinese), Scientia Sinica
Mathematica A, 2016, 46: 371 -- 408, link
- 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
- 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
- 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
- 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
- Applications of Nonstandard Analysis in Additive
Number Theory, pdf-file, The Bulletin of Symbolic
Logic, 6, No. 3 (2000), pp. 331---341.
- 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.