Israel Journal Of Mathematics Research Articles

New characterizations of the unit vector basis of or

AbstractMotivated by Altshuler’s famous characterization of the unit vector basis of $c_0$ or $\ell _p$ among symmetric bases (Altshuler [1976, Israel Journal of Mathematics, 24, 39–44]), we obtain similar characterizations among democratic bases and among bidemocratic bases. We also prove a separate characterization of the unit vector basis of $\ell _1$ .

Robust Multiplication-Based Tests for Reed–Muller Codes

We consider the following multiplication-based tests to check if a given function $f: \mathbb{F}_q^n\to \mathbb{F}_q$ is a codeword of the Reed-Muller code of dimension $n$ and order $d$ over the finite field $\mathbb{F}_q$ for prime $q$ (i.e., $f$ is the evaluation of a degree-$d$ polynomial over $\mathbb{F}_q$ for $q$ prime). * $\mathrm{Test}_{e,k}$: Pick $P_1,\ldots,P_k$ independent random degree-$e$ polynomials and accept iff the function $fP_1\cdots P_k$ is the evaluation of a degree-$(d+ek)$ polynomial (i.e., is a codeword of the Reed-Muller code of dimension $n$ and order $(d+ek)$). We prove the robust soundness of the above tests for large values of $e$, answering a question of Dinur and Guruswami [Israel Journal of Mathematics, 209:611-649, 2015]. Previous soundness analyses of these tests were known only for the case when either $e=1$ or $k=1$. Even for the case $k=1$ and $e>1$, earlier soundness analyses were not robust. We also analyze a derandomized version of this test, where (for example) the polynomials $P_1,\dots,P_k$ can be the same random polynomial $P$. This generalizes a result of Guruswami et al. [SIAM J. Comput., 46(1):132-159, 2017]. One of the key ingredients that go into the proof of this robust soundness is an extension of the standard Schwartz-Zippel lemma over general finite fields $\mathbb{F}_q$, which may be of independent interest.

The Topology-Free Construction of the Universal Type Structure for Conditional Probability Systems

We construct the universal type structure for conditional probability systems without any topological assumption, namely a type structure that is terminal, belief-complete, and non-redundant. In particular, in order to obtain the belief-completeness in a constructive way, we extend the work of Meier [An Infinitary Probability Logic for Type Spaces. Israel Journal of Mathematics, 192, 1-58] by proving strong soundness and strong completeness of an infinitary conditional probability logic with truthful and non-epistemic conditioning events.

Maryanthe Malliaris and Saharon Shelah, Cofinality spectrum problems in model theory, set theory and general topology . Journal of the American Mathematical Society, vol. 29 (2016), pp. 237–297. - Maryanthe Malliaris and Saharon Shelah, Existence of optimal ultrafilters and the fundamental complexity of simple theories . Advances in Mathematics, vol. 290 (2016), pp. 614–681. - Maryanthe Malliaris and Saharon Shelah,

Maryanthe Malliaris and Saharon Shelah, <i>Cofinality spectrum problems in model theory, set theory and general topology</i> . Journal of the American Mathematical Society, vol. 29 (2016), pp. 237–297. - Maryanthe Malliaris and Saharon Shelah, <i>Existence of optimal ultrafilters and the fundamental complexity of simple theories</i> . Advances in Mathematics, vol. 290 (2016), pp. 614–681. - Maryanthe Malliaris and Saharon Shelah,

The Topology-Free Construction of the Universal Type Structure for Conditional Probability Systems

We construct the universal type structure for conditional probability systems without any topological assumption, namely a type structure that is terminal, belief-complete, and non-redundant. In particular, in order to obtain the belief-completeness in a constructive way, we extend the work of Meier [An Infinitary Probability Logic for Type Spaces. Israel Journal of Mathematics, 192, 1-58] by proving strong soundness and strong completeness of an infinitary conditional probability logic with truthful and non-epistemic conditioning events.

André Nies. Lowness properties and randomness. Advances in Mathematics, vol. 197 (2005), no. 1, pp. 274–305. - Bjørn Kjos-Hanssen, André Nies, and Frank Stephan. Lowness for the class of Schnorr random reals. SIAM Journal on Computing, vol. 35 (2005), no. 3, pp. 647–657. - Noam Greenberg and Joseph S. Miller. Lowness for Kurtz randomness. The Journal of Symbolic Logic, vol.

André Nies. Lowness properties and randomness. Advances in Mathematics, vol. 197 (2005), no. 1, pp. 274–305. - Bjørn Kjos-Hanssen, André Nies, and Frank Stephan. Lowness for the class of Schnorr random reals. SIAM Journal on Computing, vol. 35 (2005), no. 3, pp. 647–657. - Noam Greenberg and Joseph S. Miller. Lowness for Kurtz randomness. The Journal of Symbolic Logic, vol. 74 (2009), no. 2, pp. 665–678. - Laurent Bienvenu and Joseph S. Miller. Randomness and lowness notions via open covers. Annals of Pure and Applied Logic, vol. 163 (2012), no. 5, pp. 506–518. - Johanna N. Y. Franklin, Frank Stephan, and Liang. Yu Relativizations of randomness and genericity notions. The Bulletin of the London Mathematical Society, vol. 43 (2011), no. 4, pp. 721–733. - George Barmpalias, Joseph S. Miller, and André Nies. Randomness notions and partial relativization. Israel Journal of Mathematics, vol. 191 (2012), no. 2, pp. 791–816. - Volume 19 Issue 1

Itay Neeman. Games of countable length. Sets and Proofs (Leeds, 1997), edited by S. Barry Cooper and John K. Truss, London Mathematical Society Lecture Note Series, vol. 258. Cambridge University Press, Cambridge, 1999, pp. 159-196. - Itay Neeman. Unraveling Π11sets. Annals of Pure and Applied Logic, vol. 106, no. 1–3 (2000), pp. 151-205. - Itay Neeman. Unraveling Π11sets, revisited. Israel

Itay Neeman. Games of countable length. Sets and Proofs (Leeds, 1997), edited by S. Barry Cooper and John K. Truss, London Mathematical Society Lecture Note Series, vol. 258. Cambridge University Press, Cambridge, 1999, pp. 159-196. - Itay Neeman. <i>Unraveling</i> Π₁¹<i>sets</i>. Annals of Pure and Applied Logic, vol. 106, no. 1–3 (2000), pp. 151-205. - Itay Neeman. <i>Unraveling</i> Π₁¹<i>sets, revisited</i>. Israel

Corrections to “Invariant measures and asymptotics for some skew products”, israel journal of mathematics, vol. 128, 2002, pp. 93–134

Corrections to “Invariant measures and asymptotics for some skew products”, israel journal of mathematics, vol. 128, 2002, pp. 93–134

Saharon Shelah and Hugh Woodin. Large cardinals imply that every reasonably definable set of reals is Lebesgue measurable. Israel journal of mathematics, vol. 70 (1990), pp. 381–394.

Saharon Shelah and Hugh Woodin. <i>Large cardinals imply that every reasonably definable set of reals is Lebesgue measurable</i>. <b>Israel journal of mathematics</b>, vol. 70 (1990), pp. 381–394.

Arthur W. Apter. On the least strongly compact cardinal. Israel journal of mathematics, vol. 35 (1980), pp. 225–233. - Arthur W. Apter. Measurability and degrees of strong compactness. The journal of symbolic logic, vol. 46 (1981), pp. 249–254. - Arthur W. Apter. A note on strong compactness and supercompactness. Bulletin of the London Mathematical Society, vol. 23 (1991), pp. 113–115.

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Ehud Hrushovski, A new strongly minimal set, Annals of pure and applied logic, vol. 62 (1993), pp. 147–166. - Ehud Hrushovski, Strongly minimal expansions of algebraically closed fields, Israel journal of mathematics, vol. 79 (1992), pp. 129–151.

Ehud Hrushovski, A new strongly minimal set, Annals of pure and applied logic, vol. 62 (1993), pp. 147–166. - Ehud Hrushovski, Strongly minimal expansions of algebraically closed fields, Israel journal of mathematics, vol. 79 (1992), pp. 129–151. - Volume 64 Issue 2

Moti Gitik and Saharon Shelah. Forcings with ideals and simple forcing notions. Israel journal of mathematics, vol. 68 (1989), pp. 129–160. - M. Gitik and S. Shelah. More on simple forcing notions and forcing with ideals. Annals of pure and applied logic, vol. 59 (1993), pp. 219–238. - D. H. Fremlin Real-valued-measurable cardinals. Set theory of the reals, edited by

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A. H. Lachlan. On countable stable structures which are homogeneous for a finite relational language. Israel journal of mathematics, vol. 49 (1984), pp. 69–153. - G. Cherlin and A. H. Lachlan. Stable finitely homogeneous structures. Transactions of the American Mathematical Society, vol. 296 (1986), pp. 815–850.

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Andreas Blass and Saharon Shelah. Ultrafilters with small generating sets. Israel journal of mathematics, vol. 65 (1989), pp. 259–271. - Andreas Blass and Saharon Shelah. There may be simple - and -points and the Rudin–Keisler ordering may be downward directed. Annals of pure and applied logic, vol. 33 (1987), pp. 213–243. - Andreas Blass. Near coherence of filters.

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Saharon Shelah, Can you take Solovay's inaccessible away?Israel journal of mathematics, vol. 48 (1984), pp. 1–47. - Jean Raisonnier, A mathematical proof of S. Shelah's theorem on the measure problem and related results, Israel journal of mathematics, vol. 48 (1984), pp. 48–56.

Saharon Shelah, Can you take Solovay's inaccessible away?Israel journal of mathematics, vol. 48 (1984), pp. 1–47. - Jean Raisonnier, A mathematical proof of S. Shelah's theorem on the measure problem and related results, Israel journal of mathematics, vol. 48 (1984), pp. 48–56.

Where do Israeli scientists publish?

From an analysis of papers having a first-author address in Israel and listed in 26 consecutive issues of three editions of Current Contents (CC) (July-December 1982), we have identi fied the Journals often used, the institutions contributing many papers, and the distribution of papers by subject areas. Israel's share of the world's literature is a little over 0.9% in physical. chemical and earth sciences (including mathematics). 1.0% in the life sciences (new biology). and 0.8% in engineering. tech nology and applied sciences. Technion-Israel Institute of Tech nology, Weizmann Institute of Science, and Hebrew and Tel Aviv Universities are the leading puhlishers of papers in the physical, chemical and earth sciences, whereas Hebrew Univer sity, Weizmann Institute and Tel Aviv University lead in the life sciences. Technion leads the field in engineering publica tions. followed by Ben Gurion and Tel Aviv Universities. Most Israeli papers are published in US, UK and Dutch journals. followed by Israeli and Swiss journals. The 1820 papers in our sample appeared in over 740 journals. More than 36% Israeli papers in CC (PCE) and over 42% of papers in CC (LS) have appeared in journals with impact factors greater than 2.0. Thin Solid Films, Journal of Chemical Physics, Physical Review B. Biochimica Biophysica Acta, Proceedings of the National Academy of Sciences, USA are among the most used interna tional journals, while Israel Journal of Medical Science and Israel Journal of Mathematics are two national journals carry ing many papers from Israel.

Saharon Shelah. Differentially closed fields. Israel journal of mathematics, t. 16 (1973), p. 314–328.

Saharon Shelah. Differentially closed fields. Israel journal of mathematics, t. 16 (1973), p. 314–328.

Saharon Shelah. Differentially closed fields. Israel journal of mathematics, t. 16 (1973), p. 314–328.

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Richard Laver. On Fraïssé's order type conjecture. Annals of mathematics, ser. 2 vol. 93 (1971), pp. 89–111. - Richard Laver. An order type decomposition theorem. Annals of mathematics, ser. 2 vol. 98 (1973) pp. 96–119. - Richard Laver. Better-quasi-orderings and a class of trees. Studies in foundations and combinatorics, edited by Gian-Carlo Rota, Advances in mathematics supplementary studies, vol. 1,

Richard Laver. On Fraïssé's order type conjecture. Annals of mathematics, ser. 2 vol. 93 (1971), pp. 89–111. - Richard Laver. An order type decomposition theorem. Annals of mathematics, ser. 2 vol. 98 (1973) pp. 96–119. - Richard Laver. Better-quasi-orderings and a class of trees. Studies in foundations and combinatorics, edited by Gian-Carlo Rota, Advances in mathematics supplementary studies, vol. 1,

Jon Barwise and John Schlipf. On recursively saturated models of arithmetic. Model theory and algebra, A memorial tribute to Abraham Robinson, edited by D. H. Saracino and V. B. Weispfenning, Lecture notes in mathematics, vol. 498, Springer-Verlag, Berlin, Heidelberg, and New York, 1975, pp. 42–55. - Patrick Cegielski, Kenneth McAloon, and George Wilmers. Modèles récursivement saturés de l'addition et de

Jon Barwise and John Schlipf. On recursively saturated models of arithmetic. Model theory and algebra, A memorial tribute to Abraham Robinson, edited by D. H. Saracino and V. B. Weispfenning, Lecture notes in mathematics, vol. 498, Springer-Verlag, Berlin, Heidelberg, and New York, 1975, pp. 42–55. - Patrick Cegielski, Kenneth McAloon, and George Wilmers. Modèles récursivement saturés de l'addition et de