The minimal tower problem is still open: A gap was found in the proof. However, the problem posed at the end of the issue is still open and very much related to the minimal tower problem. Solutions are welcome
*** Note the comment above ***
This is a special issue dedicated to the announcement of Shelah's recent solution of the Minimal Tower problem, one of the oldest and most important problems in infinite combinatorics which also motivated some new studies in SPM (see fourth issue of this bulletin). We give some background and personal perspectives on the problem and its solution.
We decided not to include additional research announcements in this issue, so to let them draw the attention they deserve in the coming issue.
This issue also contains an interesting new problem which is related to the Minimal Tower problem (but still open).
We announce the solution of 4+21+1/2 (!) problems posed in earlier issues of the SPM Bulletin; the ``1/2'' standing for a ``consistently yes'' answer of Zdomsky to the last issue's Problem of the Month.
This festive issue concludes the civilian year 2008 with details on a special issue of Topology and its Applications dedicated to SPM, and with a quite large list of research announcements.
This is the first issue of a semi-formal bulletin dealing with Selection Principles in Mathematics (SPM) -- this field deals with all sorts of studies of diagonalization arguments, especially in topology (covering properties, sequences of covers, etc.) and infinite combinatorics (cardinal characteristics of the continuum), and their applications to other areas of mathematics (function spaces, game theory, group theory, etc.)
This is the second issue of the SPM Bulletin (SPM stands for "Selection Principles in Mathematics"). The first issue is math.GN/0301011 and contains some background and details.
This issue contains announcements of articles on: The Pytkeev property; Partial order embeddings; Resolvability; Singular density; P(w)/fin and the Calkin algebra; Everywhere meagre and everywhere null sets; almost disjoint families; forcing axioms; Splitting families; Sacks Reals; unconditionally closed and algebraic sets in groups; Stratifiability; Dissipated Compacta; partition relations; pi-bases; covering by translates of a compact nullsets; and a new Problem of the Issue.
After a long break, we are back with some very interesting research announcements and an open problem which is one of the most difficult, long lasting, and important problems in the field. A major change in this bulletin is that from now on it will usually not appear monthly, but more close to quarterly. Special announcements (if urgent) will be made by text emails. Contributions to the next issue are, as always, welcome.
In this issue we announce a fascinating series of works on the comparison of various types of convergence of sequences of functions. Some of these properties are provably related to some of the properties which were introduced in the earlier issues of the SPM Bulletin, and many problems remain open. Section 2, written by Lev Bukovský, contains a brief survey of some of the major open problems in this area. This issue gives the first example of the importance of the transmission of knowledge between the recipients of this bulletin: One of the announcements implies a solution to one of the probl…
This issue contains a number of abstracts of papers directly related to selection principles, some of which presented at the conference SPMC2012, and the announcement of the solution of Malyhin's Problem.
This issue of the SPM Bulletin announces two conferences which are of interest to anyone working in SPM or general topology. In the second announced conference it is planned to have a significant part devoted to SPM. Those who are interested in participating should contact Ljubisa D. R. Kocinac at lkocinac@ptt.yu Kocinac is a very active mathematician in the field of SPM. We announce here one of his most recent works. The first issues of this bulletin, contain general information (first issue), basic definitions, research announcements, and open problems (all issues).
1. A Wikipedia entry on topological games 2. On a fragment of the universal Baire property for sigma^1_2 sets 3. The coarse classification of homogeneous ultra-metric spaces 4. Ramsey-like embeddings 5. Proper and piecewise proper families of reals 6. Measures and their random reals 7. Obtainable Sizes of Topologies on Finite Sets 8. Spaces of R-places of rational function fields 9. All properties in the Scheepers Diagram are linearly-sigma-additive.
This issue surveys some of the activities in the field since the previous issue, and announces a conference fully dedicated to the topic of selection principles.
In addition to announcements of several new papers, this issue contains a brief personal memorandum for Misha Matveev. The issue also announces the coming SPM meeting (June 2012).
In addition to research announcements, this issue features a call for papers to a Topology and its Applications special issue, and an intriguing open problem.
Contents: 1. Editor's note; 2. Personal impressions from the SPM07 meeting; 3. Research announcements; 3.1. Coloring ordinals by reals; 3.2. Long Borel Hierarchies; 3.3. Rothberger's property in finite powers; 3.4. Special subsets of the reals and tree forcing notions; 3.5. All automorphisms of the Calkin algebra are inner; 3.6. Continuous selections and sigma-spaces; 3.7. On the closure of the diagonal of a T1-space; 3.8. Splitting families and Noetherian type; 3.9. Even more simple cardinal invariants; 3.10. A classification of CO spaces which are continuous images of compact ordered spaces;…
This is the 34th issue of this bulletin, dedicated to selection principles in mathematics. Announcements include, among other things, a call for papers for the Topology and its Applications special issue on selection principles, and the solution of the minimal tower problem in a surprising way.
Contents of this issue: Workshops on SPM themes; Second workshop on Coverings, Selections and Games in Topology (SPM05); Analysis and Descriptive Set Theory Workshop; Descriptive set theory: Effective methods, equivalence relations; Analysis: typical functions, level sets structure; Organizational and additional details; Research announcements; Cardinal restrictions on some homogeneous compacta; Filters: Topological congruence relations on groups; Inverse Limits and Function Algebras; Ultrafilters and partial products of infinite cyclic groups; More on regular reduced products; Consistency of …
This issue contains, in addition to the usual contents, a special festive announcement: A book. This book by Banakh and Zdomsky seems to be the first in a planned series by these authors. We believe that the book will become a cornerstone in many future mathematical investigations, in particular in the field of infinite-combinatorial topology. The book's preliminary version is available online, as seen in the announcement, and the readers of the SPM Bulletin are encouraged to take a look and make comments. Zdomsky has also made two detailed contributions to this issue. This is the ideal form o…
This is the ninth issue of this bulletin. CONTENTS: Proceedings of SPM Workshop; A brief remark on van der Waerden spaces; Complete ccc Boolean algebras, the order sequential topology, and a problem of von Neumann; Cardinal invariants p, t and h and real functions; A comment on p<t; On squares of spaces and F_sigma-sets; Comparing the uniformity invariants of null sets for different measures; Maximal functions and the additivity of various families of null sets; How many miles to beta(omega)? -- Approximating beta(omega) by metric-dependent compactifications; The cardinal characteristic for re…
In addition to 29 announcements in related areas, this issue contains several contributions to "core" SPM: Measurable cardinals and the cardinality of Lindelof spaces; Topological games and covering dimension; Menger's and Hurewicz's Problems: Solutions from "The Book" and refinements; Point-cofinite covers in the Laver model; Projective versions of selection principles
CONTENTS OF THE ISSUE: Hurewicz-like tests for Borel subsets of the plane; Ordered Spaces, Metric Preimages, and Function Algebras; On the independence of a generalized statement of Egoroff's theorem from ZFC, after T. Weiss; Forty annotated questions about large topological groups; Strong compactness and a partition property; Countable Borel equivalence relations and quotient Borel spaces; Decisive creatures and large continuum; Models of real-valued measurability; Hausdorff ultrafilters; Block combinatorics; Maharam's problem; Universality of uniform Eberlein compacta; Linearly ordered compa…
CONTENTS: New reals: Can live with them, can live without them; Uniform almost everywhere domination; Heredity of tau-pseudocompactness; Understanding preservation theorems: omega^omega-bounding; Classification problems in continuum theory; Residuality of families of F_sigma sets; First countable, countably compact spaces and the continuum hypothesis; Game approach to universally Kuratowski-Ulam spaces; Small Valdivia compact spaces; Canonical forms of Borel functions on the Milliken space; Complete analytic equivalence relations; The Number of Near-Coherence Classes of Ultrafilters is Either …
Never has an issue of the SPM Bulletin contained as much interesting information as this issue does. In addition to the interesting research announcements, this issue contains announcements of solutions for three open problems, one of which being a Problem of the Month in an earlier issue. CONTENTS: The Reznichenko property and the Pytkeev property in hyperspaces; Between Maharam's and von Neumann's problems; Fraisse Limits, Ramsey Theory, and Topological Dynamics of Automorphism Groups; Concerning problems about cardinal invariants on Boolean algebras; Small Locally Compact Linearly Lindelof …
In addition to a number of new developments in the field, this issue announces the completion of the special issue of Topology and its Applications, dedicated to the proceedings of the Fourth Workshop on Coverings, Selections and Games in Topology, on the occasion of Ljubiša D.R. Kočinac's 65th birthday.
Contents: 2. Invited contribution: Ultrafilters and small sets 3. Research announcements 3.1. Inverse Systems and I-Favorable Spaces 3.2. Combinatorial and hybrid principles for sigma-directed families of countable sets modulo finite 3.3. A dichotomy characterizing analytic digraphs of uncountable Borel chromatic number in any dimension 3.4. A dichotomy characterizing analytic digraphs of uncountable Borel chromatic number in any dimension 3.5. Large continuum, oracles 3.6. Borel hierarchies in infinite products of Polish spaces 3.7. A game for the Borel functions 3.8. On some problems in gene…
In the year 2014, the field of selection principles found its way into several additional, fascinating mathematical realms. The field enters the consensus as a mainstream part of set theory and topology, and as a promising direction for young researchers that are well trained in these fields. Some of the interesting developments in the field during 2014 are reported in this issue.
CONTENTS: Lecce Workshop presentations available online; Borel cardinalities below c_0; Hereditarily non-topologizable groups; A hodgepodge of sets of reals; Random gaps; Covering a bounded set of functions by an increasing chain of slaloms; Baire-one mappings contained in a usco map; Applications of k-covers II; Additivity numbers of covering properties; Combinatorial images of sets of reals and semifilter trichotomy; Another algebraic equivalent of the Continuum Hypothesis; A connection between decomposable ultrafilters and possible cofinalities II; Game Approach to Universally Kuratowski-Ul…
With the approaching TOPOSYM'16 (http://www.toposym.cz/programme.php), it is a pleasure to see selection principles gain increasing attention and becoming a standard part of topology and set theory. At least eight of the 28 speakers, and a good number of the contributed lecture speakers, made substantial contributions to this topic in their career. For some of these, SPs constitute the main topic of research in the last few years. This is in accordance with the continuous progress on the topic, some of which reported in this bulletin.
CONTENTS: A surprising covering of the real line Unions of chains in dyadic compact spaces and topological groups On the Pytkeev property in spaces of continuous functions Selection principles related to alpha_i-properties On the Kocinac alpha_i properties A new selection principle First Countable Continua and Proper Forcing The convergence space of minimal usco mappings D-forced spaces: a new approach to resolvability Resolvability of spaces having small spread or extent Resolvability and monotone normality Isomorphism of Borel full groups A Poset Hierarchy Infinite asymptotic games Elementar…
In this issue we celebrate the appearance of the proceedings of the first SPM Workshop, announce several mathematical breakthroughs, have two extended contributions by Babinkostova, and a new open problem by Kalenda. Contents: Editor's note; Proceedings of the first workshop on Coverings, Selections, and Games in Topology; A five element basis for the uncountable linear orders; Set mapping reflection; The Proper Forcing Axiom, Prikry forcing, and the Singular Cardinals Hypothesis; A solution to the L space problem and related ZFC constructions; Countable Tightness, Elementary Submodels and Hom…
Contents: 1. Editor's note; 2. gamma-sets from a weak hypothesis; 3. Research announcements; 3.1. Ultrafilters with property (s); 3.2. On a converse to Banach's Fixed Point Theorem; 3.3. Analytic groups and pushing small sets apart 3.4. Club-guessing, stationary reflection, and coloring theorems; 3.5. More on the pressing down game; 3.6. A note on discrete sets; 3.7. Antidiamond principles and topological applications; 3.8. Partitions and indivisibility properties of countable dimensional vector spaces; 3.9. Group-valued continuous functions with the topology of pointwise convergence; 3.10. St…
Contents: 1. Combinatorial and model-theoretical principles related to regularity of ultrafilters and compactness of topological spaces, I; 2. Frechet-Urysohn fans in free topological groups; 3. Packing index of subsets in Polish groups; 4. Symmetric monochromatic subsets in colorings of the Lobachevsky plane; 5. Structural Ramsey theory of metric spaces and topological dynamics of isometry groups; 6. Distinguishing Number of Countable Homogeneous Relational Structures; 7. Indestructible colourings and rainbow Ramsey theorems; 8. Products of Borel subgroups; 9. Selection theorems and treeabili…
Contents of the issue: Selection Principles and special sets of reals: Open problems Winning the pressing down game but not Banach Mazur Ramsey classes of topological and metric spaces More on partitioning triples of countable ordinals Countable compact Hausdorff spaces need not be metrizable in ZF Every topological group is a group retract of a minimal group The complexity of classifying separable Banach spaces up to isomorphism Reals n-generic relative to some perfect tree Nagata's conjecture and countably compactifications in generic extensions A Class of Groups in Which All Unconditionally…
CONTENTS: On Selective screenability and examples of R. Pol. Workshops and conferences: The Oxford Conference on Topology and Computer Science in Honour of Peter Collins and Mike Reed; Boise Extravaganza In Set Theory (BEST2006). Research announcements: The isometry group of the Urysohn space as a Levy group; Chasing Silver; Disjoint Non-Free Subgoups of Abelian Groups; Characterizing metric spaces whose hyperspaces are absolute neighborhood retracts; A Vitali set can be homeomorphic to its complement; o-Boundedness of free objects over a Tychonoff space; On the consistency strength of the Mil…
Contents: 1. Editor's note 2. Research announcements 2.1. Pseudocompact group topologies with no infinite compact subsets 2.2. Selective coideals on (FIN[1]k) 2.3. Entire functions mapping uncountable dense sets of reals onto each other monotonically 2.4. Effective refining of Borel coverings 2.5. Symmetry and colorings: Some results and open problems 2.6. Many partition relations below density 2.7. Lindelof indestructibility, topological games and selection principles 2.8. Locally precompact groups: (Local) realcompactness and connectedness 2.9. The group Aut is Roelcke precompact 2.10. An in…
