borel ideals
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2021 ◽  
pp. 1-18
Author(s):  
Eduardo Camps-Moreno ◽  
Craig Kohne ◽  
Eliseo Sarmiento ◽  
Adam Van Tuyl
Keyword(s):  

2021 ◽  
pp. 102976
Author(s):  
Pratulananda Das ◽  
Rafał Filipów ◽  
Szymon Gła̧b ◽  
Jacek Tryba
Keyword(s):  

Author(s):  
Michael DiPasquale ◽  
Babak Jabbar Nezhad
Keyword(s):  

2020 ◽  
Vol 35 (1) ◽  
pp. 131
Author(s):  
Bahareh Lajmiri ◽  
Farhad Rahmati

In this paper, we have studied the stability of $t$-spread principal Borel ideals in degree two. We have proved that $\Ass^\infty(I) =\Min(I)\cup \{\mathfrak{m}\}$ , where $I=B_t(u)\subset S$ is a $t$-spread Borel ideal generated in degree $2$ with $u=x_ix_n, t+1\leq i\leq n-t.$ Indeed, $I$ has the property that $\Ass(I^m)=\Ass(I)$ for all $m\geq 1$ and $i\leq t,$ in other words, $I$ is normally torsion free. Moreover, we have shown that $I$ is a set theoretic complete intersection if and only if $u=x_{n-t}x_n$. Also, we have derived some results on the vanishing of Lyubeznik numbers of these ideals.  


2019 ◽  
Vol 116 (38) ◽  
pp. 18883-18887 ◽  
Author(s):  
David Schrittesser ◽  
Asger Törnquist

We show that if all collections of infinite subsets of N have the Ramsey property, then there are no infinite maximal almost disjoint (mad) families. The implication is proved in Zermelo–Fraenkel set theory with only weak choice principles. This gives a positive solution to a long-standing problem that goes back to Mathias [A. R. D. Mathias, Ann. Math. Logic 12, 59–111 (1977)]. The proof exploits an idea which has its natural roots in ergodic theory, topological dynamics, and invariant descriptive set theory: We use that a certain function associated to a purported mad family is invariant under the equivalence relation E0 and thus is constant on a “large” set. Furthermore, we announce a number of additional results about mad families relative to more complicated Borel ideals.


2019 ◽  
Vol 100 (1) ◽  
pp. 48-57 ◽  
Author(s):  
SHAMILA BAYATI ◽  
IMAN JAHANI ◽  
NADIYA TAGHIPOUR

We investigate whether the property of having linear quotients is inherited by ideals generated by multigraded shifts of a Borel ideal and a squarefree Borel ideal. We show that the ideal generated by the first multigraded shifts of a Borel ideal has linear quotients, as do the ideal generated by the $k$th multigraded shifts of a principal Borel ideal and an equigenerated squarefree Borel ideal for each $k$. Furthermore, we show that equigenerated squarefree Borel ideals share the property of being squarefree Borel with the ideals generated by multigraded shifts.


2019 ◽  
Vol 112 (6) ◽  
pp. 587-597 ◽  
Author(s):  
Claudia Andrei ◽  
Viviana Ene ◽  
Bahareh Lajmiri
Keyword(s):  

2018 ◽  
Vol 152 (1) ◽  
pp. 141-163 ◽  
Author(s):  
Francisco Guevara ◽  
Carlos Uzcátegui
Keyword(s):  

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