On long increasing chains modulo flat ideals

We prove that, e.g., in ^{(ω 3)}(ω 3) there is no sequence of length W4 increasing modulo the ideal of countable sets (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some Independence Results on Reflection

It is proved that there is a certain degree of independencebetween stationary reflection phenomena at different cofinalities.     

On T 3-Topological Space Omitting Many Cardinals

We prove that for every (infinite cardinal) there is a T ₃-space X with clopen basis, points such that every closed subspace of cardinality < has cardinality < .     

Characterizing Automorphism Groups of Ordered Abelian Groups

A proof is given of the following theorem, which characterizesfull automorphism groups of ordered abelian groups: a groupH is the automorphism group of some ordered abelian group ifand only if H is right-orderable. 2000 Mathematics Subject Classification20K15, 20K20, 20F60, 20K30 (primary); 03E05 (secondary).     

Strongly meager and strong measure zero sets

 In this paper we present two consistency results concerning the existence of large strong measure zero and strongly meager sets. RID="ID=" <E5>Mathematics Subject Classification (2000):</E5>&ensp;03E35 RID="ID=" The first author was supported by Alexander von Humboldt Foundation and NSF grant DMS 95-05375. The second author was partially supported by Basic Research Fund, Israel Academy of Sciences, publication 658 Received: 6 January 1999 / Revised version: 20 July 1999 / Published online: 25 February 2002 RID=" ID=" <E5>Mathematics Subject Classification (2000):</E5>&ensp;03E35 RID=" ID=" The first author was supported by Alexander von Humboldt Foundation and NSF grant DMS 95-05375. The second author was partially supported by Basic Research Fund, Israel Academy of Sciences, publication 658     

Models with second order properties. III. Omitting types forL(Q)

We generalize Keisler's omitting types theorem forL(Q) in the ₁-interpretation, to most cases in which Chang's two cardinal theorem applies. As an application we answer positively a question of Magidor and Malitz on the compactness of their logic in cardinalities higher than ₁.     

Very weak zero one law for random graphs with order and random binary functions

Natural languages and random structures are given for which there are sentences A with no limit probability, yet for every A the difference between the probabilities that A holds on random structures of sizes n and n + 1 approaches zero with n. © 1996 John Wiley & Sons, Inc. Random Struct. Alg., 9, 351–358 (1996)     

♣ Does not imply the existence of a Suslin tree

We prove that ♣ does not imply the existence of a Suslin tree, so answering a question of I. Juhász. The authors thank the Israel Academy of Sciences and Humanities for partial support through the Basic Research Foundation Grant number 0327398. Mirna Džamonja would in addition like to thank The Hebrew University of Jerusalem and The Lady Davis Foundation for the Forchheimer Postdoctoral Fellowship during the academic year 1994/95, and Rutgers University for their hospitality during a visit in November 1995, when part of the research for this paper was conducted. Some of the research was also conducted while Mirna Džamonja was a visiting assistant professor at the University of Wisconsin-Madison. This publication is denoted [DjSh 604] in the list of publications of Saharon Shelah.     

Non-special Aronszajn trees on ℵω+1

We continue our research on the relative strength ofL-like combinatorial principles for successors of singular cardinals. In [3] we have shown that the existence of a λ⁺-special Aronszajn tree does not follow from that of a λ⁺-Souslin tree. It follows from [5], [4] and [6] that under G.C.H. □_λ does imply the existence of a λ⁺-Souslin tree. In [2] we show that □_λ does not follow from the existence of a λ⁺-special Aronszajn tree. Here we show that the existence of such a tree implies that of an ‘almost Souslin’ λ⁺-tree. It follows that the statement “All λ⁺-Aronszajn trees are special” implies that there are no λ⁺-Aronszajn trees.     

Homogeneous almost disjoint families

An almost disjoint family is constructed which is isomorphic to any almost disjoint family which can be constructed from it by taking subsets and finite unions. This is applied to the construction of a Boolean algebra with related properties.Presented by R. McKenzie.Partially supported by Israel-US Binational Research Fund.Partially supported by NSERC.