Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals
Search results

Search: MSC category 03 ( Mathematical logic and foundations )

 Expand all        Collapse all Results 1 - 20 of 20

1. CMB 2014 (vol 57 pp. 579)

Larson, Paul; Tall, Franklin D.
 On the Hereditary Paracompactness of Locally Compact, Hereditarily Normal Spaces We establish that if it is consistent that there is a supercompact cardinal, then it is consistent that every locally compact, hereditarily normal space which does not include a perfect pre-image of $\omega_1$ is hereditarily paracompact. Keywords:locally compact, hereditarily normal, paracompact, Axiom R, PFA$^{++}$Categories:54D35, 54D15, 54D20, 54D45, 03E65, 03E35

2. CMB 2013 (vol 57 pp. 119)

Mildenberger, Heike; Raghavan, Dilip; Steprans, Juris
 Splitting Families and Complete Separability We answer a question from Raghavan and SteprÄns by showing that $\mathfrak{s} = {\mathfrak{s}}_{\omega, \omega}$. Then we use this to construct a completely separable maximal almost disjoint family under $\mathfrak{s} \leq \mathfrak{a}$, partially answering a question of Shelah. Keywords:maximal almost disjoint family, cardinal invariantsCategories:03E05, 03E17, 03E65

3. CMB 2013 (vol 57 pp. 631)

Sokić, Miodrag
 Indicators, Chains, Antichains, Ramsey Property We introduce two Ramsey classes of finite relational structures. The first class contains finite structures of the form $(A,(I_{i})_{i=1}^{n},\leq ,(\preceq _{i})_{i=1}^{n})$ where $\leq$ is a total ordering on $A$ and $% \preceq _{i}$ is a linear ordering on the set $\{a\in A:I_{i}(a)\}$. The second class contains structures of the form $(A,\leq ,(I_{i})_{i=1}^{n},\preceq )$ where $(A,\leq )$ is a weak ordering and $% \preceq$ is a linear ordering on $A$ such that $A$ is partitioned by $% \{a\in A:I_{i}(a)\}$ into maximal chains in the partial ordering $\leq$ and each $\{a\in A:I_{i}(a)\}$ is an interval with respect to $\preceq$. Keywords:Ramsey property, linear orderingsCategories:05C55, 03C15, 54H20

4. CMB 2012 (vol 57 pp. 61)

Geschke, Stefan
 2-dimensional Convexity Numbers and $P_4$-free Graphs For $S\subseteq\mathbb R^n$ a set $C\subseteq S$ is an $m$-clique if the convex hull of no $m$-element subset of $C$ is contained in $S$. We show that there is essentially just one way to construct a closed set $S\subseteq\mathbb R^2$ without an uncountable $3$-clique that is not the union of countably many convex sets. In particular, all such sets have the same convexity number; that is, they require the same number of convex subsets to cover them. The main result follows from an analysis of the convex structure of closed sets in $\mathbb R^2$ without uncountable 3-cliques in terms of clopen, $P_4$-free graphs on Polish spaces. Keywords:convex cover, convexity number, continuous coloring, perfect graph, cographCategories:52A10, 03E17, 03E75

5. CMB 2012 (vol 56 pp. 709)

Bartošová, Dana
 Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures It is a well-known fact, that the greatest ambit for a topological group $G$ is the Samuel compactification of $G$ with respect to the right uniformity on $G.$ We apply the original description by Samuel from 1948 to give a simple computation of the universal minimal flow for groups of automorphisms of uncountable structures using FraÃ¯ssÃ© theory and Ramsey theory. This work generalizes some of the known results about countable structures. Keywords:universal minimal flows, ultrafilter flows, Ramsey theoryCategories:37B05, 03E02, 05D10, 22F50, 54H20

6. CMB 2011 (vol 56 pp. 564)

Herzog, Ivo
 Ziegler's Indecomposability Criterion Ziegler's Indecomposability Criterion is used to prove that a totally transcendental, i.e., $\Sigma$-pure injective, indecomposable left module over a left noetherian ring is a directed union of finitely generated indecomposable modules. The same criterion is also used to give a sufficient condition for a pure injective indecomposable module ${_R}U$ to have an indecomposable local dual $U_R^{\sharp}.$ Keywords:pure injective indecomposable module, local dual, generic module, amalgamationCategories:16G10, 03C60

7. CMB 2011 (vol 56 pp. 317)

Dorais, François G.
 A Note on Conjectures of F. Galvin and R. Rado In 1968, Galvin conjectured that an uncountable poset $P$ is the union of countably many chains if and only if this is true for every subposet $Q \subseteq P$ with size $\aleph_1$. In 1981, Rado formulated a similar conjecture that an uncountable interval graph $G$ is countably chromatic if and only if this is true for every induced subgraph $H \subseteq G$ with size $\aleph_1$. TodorÄeviÄ has shown that Rado's Conjecture is consistent relative to the existence of a supercompact cardinal, while the consistency of Galvin's Conjecture remains open. In this paper, we survey and collect a variety of results related to these two conjectures. We also show that the extension of Rado's conjecture to the class of all chordal graphs is relatively consistent with the existence of a supercompact cardinal. Keywords:Galvin conjecture, Rado conjecture, perfect graph, comparability graph, chordal graph, clique-cover number, chromatic numberCategories:03E05, 03E35, 03E55

8. CMB 2011 (vol 56 pp. 203)

Tall, Franklin D.
 Productively LindelÃ¶f Spaces May All Be $D$ We give easy proofs that (a) the Continuum Hypothesis implies that if the product of $X$ with every LindelÃ¶f space is LindelÃ¶f, then $X$ is a $D$-space, and (b) Borel's Conjecture implies every Rothberger space is Hurewicz. Keywords:productively LindelÃ¶f, $D$-space, projectively $\sigma$-compact, Menger, HurewiczCategories:54D20, 54B10, 54D55, 54A20, 03F50

9. CMB 2011 (vol 55 pp. 378)

Oman, Greg; Salminen, Adam
 On Modules Whose Proper Homomorphic Images Are of Smaller Cardinality Let $R$ be a commutative ring with identity, and let $M$ be a unitary module over $R$. We call $M$ H-smaller (HS for short) if and only if $M$ is infinite and $|M/N|<|M|$ for every nonzero submodule $N$ of $M$. After a brief introduction, we show that there exist nontrivial examples of HS modules of arbitrarily large cardinality over Noetherian and non-Noetherian domains. We then prove the following result: suppose $M$ is faithful over $R$, $R$ is a domain (we will show that we can restrict to this case without loss of generality), and $K$ is the quotient field of $R$. If $M$ is HS over $R$, then $R$ is HS as a module over itself, $R\subseteq M\subseteq K$, and there exists a generating set $S$ for $M$ over $R$ with $|S|<|R|$. We use this result to generalize a problem posed by Kaplansky and conclude the paper by answering an open question on JÃ³nsson modules. Keywords:Noetherian ring, residually finite ring, cardinal number, continuum hypothesis, valuation ring, JÃ³nsson moduleCategories:13A99, 13C05, 13E05, 03E50

10. CMB 2010 (vol 54 pp. 270)

Dow, Alan
 Sequential Order Under PFA It is shown that it follows from PFA that there is no compact scattered space of height greater than $\omega$ in which the sequential order and the scattering heights coincide. Keywords:sequential order, scattered spaces, PFACategories:54D55, 03E05, 03E35, 54A20

11. CMB 2010 (vol 53 pp. 286)

Gorelic, Isaac
 Orders of π-Bases We extend the scope of B. Shapirovskii's results on the order of $\pi$-bases in compact spaces and answer some questions of V. Tkachuk. Keywords:Shapirovskii π-base, point-countable π-base, free sequences, canonical form for ordinalsCategories:54A25, 03E10, 03E75, 54A35

12. CMB 2009 (vol 53 pp. 64)

Dodos, Pandelis
 On Antichains of Spreading Models of Banach Spaces We show that for every separable Banach space $X$, either $\mathrm{SP_w}(X)$ (the set of all spreading models of $X$ generated by weakly-null sequences in $X$, modulo equivalence) is countable, or $\mathrm{SP_w}(X)$ contains an antichain of the size of the continuum. This answers a question of S.~J. Dilworth, E. Odell, and B. Sari. Categories:46B20, 03E15

13. CMB 2009 (vol 52 pp. 303)

Shelah, Saharon
 A Comment on $\mathfrak{p} < \mathfrak{t}$'' Dealing with the cardinal invariants ${\mathfrak p}$ and ${\mathfrak t}$ of the continuum, we prove that ${\mathfrak m}={\mathfrak p} = \aleph_2\ \Rightarrow\ {\mathfrak t} =\aleph_2$. In other words, if ${\bf MA}_{\aleph_1}$ (or a weak version of this) holds, then (of course $\aleph_2\le {\mathfrak p}\le {\mathfrak t}$ and) ${\mathfrak p}=\aleph_2\ \Rightarrow\ {\mathfrak p}={\mathfrak t}$. The proof is based on a criterion for ${\mathfrak p}<{\mathfrak t}$. Categories:03E17, 03E05, 03E50

14. CMB 2009 (vol 52 pp. 127)

Shelah, Saharon
 The Erd\H{o}s--Rado Arrow for Singular Cardinals We prove in ZFC that if $\cf(\lambda)>\aleph_0$ and $2^{\cf (\lambda)}<\lambda$, then $\lambda \rightarrow (\lambda,\omega+1)^2$. Keywords:set theory, partition calculusCategory:03E20

15. CMB 2008 (vol 51 pp. 579)

Matet, Pierre
 Guessing with Mutually Stationary Sets We use the mutually stationary sets of Foreman and Magidor as a tool to establish the validity of the two-cardinal version of the diamond principle in some special cases. Keywords:$P_\kappa(\lambda)$, diamond principleCategory:03E05

16. CMB 2008 (vol 51 pp. 593)

Ros{\l}anowski, Andrzej; Stepr\={a}ns, Juris
 Chasing Silver We show that limits of CS iterations of the $n$-Silver forcing notion have the $n$-localization property. Keywords:$n$-localization property, the Silver forcing, CS iterationsCategories:03E40, 03E35

17. CMB 2007 (vol 50 pp. 519)

Henson, C. Ward; Raynaud, Yves; Rizzo, Andrew
 On Axiomatizability of Non-Commutative $L_p$-Spaces It is shown that Schatten $p$-classes of operators between Hilbert spaces of different (infinite) dimensions have ultrapowers which are (completely) isometric to non-commutative $L_p$-spaces. On the other hand, these Schatten classes are not themselves isomorphic to non-commutative $L_p$ spaces. As a consequence, the class of non-commutative $L_p$-spaces is not axiomatizable in the first-order language developed by Henson and Iovino for normed space structures, neither in the signature of Banach spaces, nor in that of operator spaces. Other examples of the same phenomenon are presented that belong to the class of corners of non-commutative $L_p$-spaces. For $p=1$ this last class, which is the same as the class of preduals of ternary rings of operators, is itself axiomatizable in the signature of operator spaces. Categories:46L52, 03C65, 46B20, 46L07, 46M07

18. CMB 2002 (vol 45 pp. 71)

van den Dries, Lou; Kuhlmann, Franz-Viktor
 Images of Additive Polynomials in $\FF_q ((t))$ Have the Optimal Approximation Property We show that the set of values of an additive polynomial in several variables with arguments in a formal Laurent series field over a finite field has the optimal approximation property: every element in the field has a (not necessarily unique) closest approximation in this set of values. The approximation is with respect to the canonical valuation on the field. This property is elementary in the language of valued rings. Categories:12J10, 12L12, 03C60

19. CMB 2000 (vol 43 pp. 397)

Bonato, Anthony; Cameron, Peter; Delić, Dejan
 Tournaments and Orders with the Pigeonhole Property A binary structure $S$ has the pigeonhole property ($\mathcal{P}$) if every finite partition of $S$ induces a block isomorphic to $S$. We classify all countable tournaments with ($\mathcal{P}$); the class of orders with ($\mathcal{P}$) is completely classified. Keywords:pigeonhole property, tournament, orderCategories:05C20, 03C15

20. CMB 1999 (vol 42 pp. 13)

Brendle, Jörg
 Dow's Principle and $Q$-Sets A $Q$-set is a set of reals every subset of which is a relative $G_\delta$. We investigate the combinatorics of $Q$-sets and discuss a question of Miller and Zhou on the size $\qq$ of the smallest set of reals which is not a $Q$-set. We show in particular that various natural lower bounds for $\qq$ are consistently strictly smaller than $\qq$. Keywords:$Q$-set, cardinal invariants of the continuum, pseudointersection number, $\MA$($\sigma$-centered), Dow's principle, almost disjoint family, almost disjointness principle, iterated forcingCategories:03E05, 03E35, 54A35

© Canadian Mathematical Society, 2015 : https://cms.math.ca/