Menachem Kojman
Research Subjects
Research Interests
Menachem Kojman has a total of 39 co-authors. Here are the top co-authors by number of shared publications:
- Saharon Shelah
The Hebrew University of Jerusalem
17 shared publications Martin Goldstern
Algebra, TU Wien, Wiedner Hauptstrasse 8-10/104, A-1040 Vienna, Austria
3 shared publicationsStefan Geschke
Universität Berlin
3 shared publications- Wiesław Kubiś
Institute of Mathematics, Czech Academy of Sciences, Prague, Czech Republic
3 shared publications - Andrea Cantini
Department of Philosophy Università degli Studi di Firenze Via Bolognese 52 I-50139 Firenze Italy
2 shared publications - Bernard Linsky
Univ Alberta, Philosophy, Edmonton, AB T6G 2E5, Canada
2 shared publications
Latest Publications
- 14 August 2018
- Published by Springer Nature in Combinatorica
- Vol. 39 (3) , 659-678
Partitioning Subgraphs of Profinite Ordered Graphs
- 14 August 2018
- Published by Springer Nature in Combinatorica
- Vol. 39 (3) , 659-678
Partitioning Subgraphs of Profinite Ordered Graphs
- Open Access
- 1 December 2017
- Published by Cambridge University Press (CUP) in The Bulletin of Symbolic Logic
- Vol. 23 (4) , f1-f3
BSL volume 23 issue 4 Cover and Front matter
The BULLETIN, the JOURNAL and the REVIEW OF SYMBOLIC LOGIC are the official organs of the Association for Symbolic Logic, an international organization for furthering research in logic and the exchange of ideas among mathematicians, computer scientists, linguists, and others interested in this fi eld. The BULLETIN encourages submissions of Articles and Communications in all areas of logic, including mathematical or philosophical logic, logic in computer science or linguistics, the history or philosophy of logic, and applications of logic to other fields. The BULLETIN also publishes reviews of publications in logic. Editors
- 1 December 2017
- Published by Cambridge University Press (CUP) in The Bulletin of Symbolic Logic
- Vol. 23 (4) , f1-f3
Open AccessBSL volume 23 issue 4 Cover and Front matter
The BULLETIN, the JOURNAL and the REVIEW OF SYMBOLIC LOGIC are the official organs of the Association for Symbolic Logic, an international organization for furthering research in logic and the exchange of ideas among mathematicians, computer scientists, linguists, and others interested in this fi eld. The BULLETIN encourages submissions of Articles and Communications in all areas of logic, including mathematical or philosophical logic, logic in computer science or linguistics, the history or philosophy of logic, and applications of logic to other fields. The BULLETIN also publishes reviews of publications in logic. Editors
- Open Access
- 21 June 2017
- Published by Cambridge University Press (CUP) in The Bulletin of Symbolic Logic
- Vol. 23 (2) , f1-f3
BSL volume 23 issue 2 Cover and Front matter
Please follow the submission procedure described at http://www.aslonline.org/journals-bulletin-guide.html It is recommended that papers be prepared in L A T E X using the ASL's class fi le, especially for manuscripts having extensive symbolic or mathematical notation. This style fi le is available from the ASL's website at http://www.aslonline.org; links from that site provide further information about the BULLETIN and about submitting papers for publication. No print offprints will be supplied but authors will receive a link to a freely accessible electronic pdf of their published article. Print offprints may be purchased if required. Articles present topics of broad interest in a way that is accessible to a large audience. They can be purely expository, survey, or historical articles or they may contain, in addition, new ideas or results or new approaches to old ones. Communications should be announcements of important new results and ideas in any aspect of logic; they may be short papers in their fi nal form or preliminary announcements (extended abstracts, position papers) of longer, full papers that will be published elsewhere. In any case, they should include, in addition to a description of the new results or ideas, enough history, background, and explanation to make the significance of the work apparent to a wide audience. Communications will be quickly refereed and published within six months of the submission of fi nal version. Books for review in the BULLETIN should be sent to ASL,
- 21 June 2017
- Published by Cambridge University Press (CUP) in The Bulletin of Symbolic Logic
- Vol. 23 (2) , f1-f3
Open AccessBSL volume 23 issue 2 Cover and Front matter
Please follow the submission procedure described at http://www.aslonline.org/journals-bulletin-guide.html It is recommended that papers be prepared in L A T E X using the ASL's class fi le, especially for manuscripts having extensive symbolic or mathematical notation. This style fi le is available from the ASL's website at http://www.aslonline.org; links from that site provide further information about the BULLETIN and about submitting papers for publication. No print offprints will be supplied but authors will receive a link to a freely accessible electronic pdf of their published article. Print offprints may be purchased if required. Articles present topics of broad interest in a way that is accessible to a large audience. They can be purely expository, survey, or historical articles or they may contain, in addition, new ideas or results or new approaches to old ones. Communications should be announcements of important new results and ideas in any aspect of logic; they may be short papers in their fi nal form or preliminary announcements (extended abstracts, position papers) of longer, full papers that will be published elsewhere. In any case, they should include, in addition to a description of the new results or ideas, enough history, background, and explanation to make the significance of the work apparent to a wide audience. Communications will be quickly refereed and published within six months of the submission of fi nal version. Books for review in the BULLETIN should be sent to ASL,
- 1 November 2016
- Published by Elsevier in Topology and its Applications
- Vol. 213, 145-153
On the arithmetic of density
- 1 November 2016
- Published by Elsevier in Topology and its Applications
- Vol. 213, 145-153
On the arithmetic of density
- Open Access
On the arithmetic of density
The $\kappa$-density of a cardinal $\mu\ge\kappa$ is the least cardinality of a dense collection of $\kappa$-subsets of $\mu$ and is denoted by $\mathcal D(\mu,\kappa)$. The Singular Density Hypothesis (SDH) for a singular cardinal $\mu$ of cofinality $cf\mu=\kappa$ is the equation $\mathcal D(\mu,\kappa)=\mu^+$. The Generalized Density Hypothesis (GDH) for $\mu$ and $\lambda$ such that $\lambda\le\mu$ is: $\mathcal D(\mu,\lambda)=\mu$ if $cf\mu\not=cf\lambda$ and $\mathcal D(\mu,\lambda)=\mu^+$ if $cf\mu=cf\lambda$. Density is shown to satisfy Silver's theorem. The most important case is: Theorem 2.6. If $\kappa=cf\kappa<\theta=cf\mu<\mu$ and the set of cardinals $\lambda<\mu$ of cofinality $\kappa$ that satisfy the \textsf{SDH} is stationary in $\mu$ then the SDH holds at $\mu$. A more general version is given in Theorem 2.8 A corollary of Theorem 2.6 is: Theorem 3.2 If the Singular Density Hypothesis holds for all sufficiently large singular cardinals of some fixed cofinality $\kappa$, then for all cardinals $\lambda$ with $cf\lambda \ge \kappa$, for all sufficiently large $\mu$, the GDH holds.Open AccessOn the arithmetic of density
The $\kappa$-density of a cardinal $\mu\ge\kappa$ is the least cardinality of a dense collection of $\kappa$-subsets of $\mu$ and is denoted by $\mathcal D(\mu,\kappa)$. The Singular Density Hypothesis (SDH) for a singular cardinal $\mu$ of cofinality $cf\mu=\kappa$ is the equation $\mathcal D(\mu,\kappa)=\mu^+$. The Generalized Density Hypothesis (GDH) for $\mu$ and $\lambda$ such that $\lambda\le\mu$ is: $\mathcal D(\mu,\lambda)=\mu$ if $cf\mu\not=cf\lambda$ and $\mathcal D(\mu,\lambda)=\mu^+$ if $cf\mu=cf\lambda$. Density is shown to satisfy Silver's theorem. The most important case is: Theorem 2.6. If $\kappa=cf\kappa<\theta=cf\mu<\mu$ and the set of cardinals $\lambda<\mu$ of cofinality $\kappa$ that satisfy the \textsf{SDH} is stationary in $\mu$ then the SDH holds at $\mu$. A more general version is given in Theorem 2.8 A corollary of Theorem 2.6 is: Theorem 3.2 If the Singular Density Hypothesis holds for all sufficiently large singular cardinals of some fixed cofinality $\kappa$, then for all cardinals $\lambda$ with $cf\lambda \ge \kappa$, for all sufficiently large $\mu$, the GDH holds. - 1 January 2015
- Published by Elsevier in Advances in Mathematics
- Vol. 269, 707-725
Splitting families of sets in ZFC
- 1 January 2015
- Published by Elsevier in Advances in Mathematics
- Vol. 269, 707-725
Splitting families of sets in ZFC
- 23 July 2014
- Published by Springer Nature in Israel Journal of Mathematics
- Vol. 202 (1) , 195-225
Noetherian type in topological products
- 23 July 2014
- Published by Springer Nature in Israel Journal of Mathematics
- Vol. 202 (1) , 195-225
Noetherian type in topological products
- 7 February 2014
- Published by Springer Nature in Israel Journal of Mathematics
- Vol. 201 (2) , 585-592
Shelah’s revised GCH theorem and a question by Alon on infinite graphs colorings
- 7 February 2014
- Published by Springer Nature in Israel Journal of Mathematics
- Vol. 201 (2) , 585-592
Shelah’s revised GCH theorem and a question by Alon on infinite graphs colorings
- Open Access
Splitting families of sets in ZFC
Miller's 1937 splitting theorem was proved for pairs of cardinals $(\n,\rho)$ in which $n$ is finite and $\rho$ is infinite. An extension of Miller's theorem is proved here in ZFC for pairs of cardinals $(\nu,\rho)$ in which $\nu$ is arbitrary and $\rho\ge \beth_\om(\nu)$. The proof uses a new general method that is based on Shelah's revises Generalized Continuum Hypothesis theorem. Upper bounds on conflict-free coloring numbers of families of sets and a general comparison theorem follow as corollaries of the main theorem. Other corollaries eliminate the use of additional axioms from splitting theorems due to Erdos, Hajnal, Komjath, Juhasz and Shelah.Open AccessSplitting families of sets in ZFC
Miller's 1937 splitting theorem was proved for pairs of cardinals $(\n,\rho)$ in which $n$ is finite and $\rho$ is infinite. An extension of Miller's theorem is proved here in ZFC for pairs of cardinals $(\nu,\rho)$ in which $\nu$ is arbitrary and $\rho\ge \beth_\om(\nu)$. The proof uses a new general method that is based on Shelah's revises Generalized Continuum Hypothesis theorem. Upper bounds on conflict-free coloring numbers of families of sets and a general comparison theorem follow as corollaries of the main theorem. Other corollaries eliminate the use of additional axioms from splitting theorems due to Erdos, Hajnal, Komjath, Juhasz and Shelah. - Open Access
Noetherian type in topological products
The cardinal invariant "Noetherian type" of a topological space $X$ (Nt(X)) was introduced by Peregudov in 1997 to deal with base properties that were studied by the Russian School as early as 1976. We study its behavior in products and box-products of topological spaces. We prove in Section 2: 1) There are spaces $X$ and $Y$ such that $Nt(X \times Y) < \min\{Nt(X), Nt(Y)\}$. 2) In several classes of compact spaces, the Noetherian type is preserved by the operations of forming a square and of passing to a dense subspace. The Noetherian type of the Cantor Cube of weight $\aleph_\omega$ with the countable box topology, $(2^{\aleph_\omega})_\delta$, is shown in Section 3 to be closely related to the combinatorics of covering collections of countable subsets of $\aleph_\omega$. We discuss the influence of principles like $\square_{\aleph_\omega}$ and Chang's conjecture for $\aleph_\omega$ on this number and prove that it is not decidable in ZFC (relative to the consistency of ZFC with large cardinal axioms). Within PCF theory we establish the existence of an $(\aleph_4,\aleph_1)$-sparse covering family of countable subsets of $\aleph_\omega$. From this follows an absolute upper bound of $\aleph_4$ on the Noetherian type of $(2^{\aleph_\omega})_\delta$. The proof uses ideas from Shelah's proof that if $\kappa^+ <\lambda$ then his ideal $I[\lambda]$ contains a stationary set consisting of points of cofinality $\kappa$.Open AccessNoetherian type in topological products
The cardinal invariant "Noetherian type" of a topological space $X$ (Nt(X)) was introduced by Peregudov in 1997 to deal with base properties that were studied by the Russian School as early as 1976. We study its behavior in products and box-products of topological spaces. We prove in Section 2: 1) There are spaces $X$ and $Y$ such that $Nt(X \times Y) < \min\{Nt(X), Nt(Y)\}$. 2) In several classes of compact spaces, the Noetherian type is preserved by the operations of forming a square and of passing to a dense subspace. The Noetherian type of the Cantor Cube of weight $\aleph_\omega$ with the countable box topology, $(2^{\aleph_\omega})_\delta$, is shown in Section 3 to be closely related to the combinatorics of covering collections of countable subsets of $\aleph_\omega$. We discuss the influence of principles like $\square_{\aleph_\omega}$ and Chang's conjecture for $\aleph_\omega$ on this number and prove that it is not decidable in ZFC (relative to the consistency of ZFC with large cardinal axioms). Within PCF theory we establish the existence of an $(\aleph_4,\aleph_1)$-sparse covering family of countable subsets of $\aleph_\omega$. From this follows an absolute upper bound of $\aleph_4$ on the Noetherian type of $(2^{\aleph_\omega})_\delta$. The proof uses ideas from Shelah's proof that if $\kappa^+ <\lambda$ then his ideal $I[\lambda]$ contains a stationary set consisting of points of cofinality $\kappa$.