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- Renling Jin
- 2001

Answering a problem posed by Keisler and Leth, we prove a theorem in non–standard analysis to reveal a phenomenon about sumsets, which says that if two sets A and B are large in terms of “measure”,… (More)

- Renling Jin
- 2011

Plünnecke proved that if B ⊆ N is a basis of order h > 1, i.e., σ(hB) = 1, then σ(A+B) > σ(A)1− 1 h where A is an arbitrary subset of N and σ represents Shnirel’man density. In this paper we explore… (More)

- Renling Jin, H. Jerome Keisler
- J. Symb. Log.
- 2000

We characterize Maharam spectra of Loeb probability spaces and give some applications of the results.

- Marc E de Perrot, Stefan Fischer, +4 authors Shaf H Keshavjee
- Transplantation
- 2001

INTRODUCTION
Prostaglandin E1 (PGE1) has been demonstrated to reduce ischemia-reperfusion (IR) injury following lung transplantation. However, the cytoprotective mechanisms remain largely unknown.… (More)

- Renling Jin
- J. Symb. Log.
- 1992

An L{structure is called internally presented in a nonstandard universe if its base set and interpretation of every symbol in L are internal. A nonstandard universe is said to satisfy the… (More)

- Renling Jin
- 2007

Let N be the set of all non-negative integers, A ⊆ N be a finite set, and 2A be the set of all numbers of the form a + b for all a and b in A. In [Fr1] the arithmetic structure of A was optimally… (More)

- Alexandre V. Borovik, Renling Jin, Mikhail G. Katz
- Notre Dame Journal of Formal Logic
- 2012

A construction of the real number system based on almost homomorphisms of the integers Z was proposed by Schanuel, Arthan, and others. We combine such a construction with the ultrapower or limit… (More)

- Renling Jin
- J. Symb. Log.
- 1997

Type two cuts, bad cuts and very bad cuts are introduced in [KL] for studying the relationship between Loeb measure and U-topology of a hyper nite time line in an !1-saturated nonstandard universe.… (More)

- Renling Jin
- 2011

We discuss whether Plünnecke’s inequality for Shnirel’man density with respect to Shnirel’man basis can be generalized to other densities with respect to other concepts of basis. We show behavioral… (More)

- Renling Jin
- J. Symb. Log.
- 2001

Answers are given to two questions concerning the existence of some sparse subsets of H = f0; 1; : : : ;H 1g N, where H is a hyper nite integer. In x1, we answer a question of Kanovei by showing that… (More)