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Generic Large Cardinals and Systems of Filters [article]

Giorgio Audrito, Silvia Steila
2017 arXiv   pre-print
In this framework we investigate the topic of definability of generic large cardinals properties.  ...  We introduce the notion of C-system of filters, generalizing the standard definitions of both extenders and towers of normal ideals.  ...  We would like to thank Matteo Viale for his valuable suggestions, remarks and corrections; and for addressing us to the topic of generic large cardinals in the first place.  ... 
arXiv:1511.05326v2 fatcat:idqwlvdvj5filhidsa3dkmant4

GENERIC LARGE CARDINALS AND SYSTEMS OF FILTERS

GIORGIO AUDRITO, SILVIA STEILA
2017 Journal of Symbolic Logic (JSL)  
In this framework we investigate the topic of definability of generic large cardinals properties.  ...  We introduce the notion of ${\cal C}$ -system of filters, generalizing the standard definitions of both extenders and towers of normal ideals.  ...  We would like to thank Matteo Viale for his valuable suggestions, remarks and corrections; and for addressing us to the topic of generic large cardinals in the first place.  ... 
doi:10.1017/jsl.2017.27 fatcat:ng4kiv2umzf7detpfbdq5lyopa

Large cardinals and continuity of coordinate functionals of filter bases in Banach spaces [article]

Tomasz Kania, Jarosław Swaczyna
2020 arXiv   pre-print
In particular, this applies to the filter of statistical convergence, thereby we solve a problem by V. Kadets (at least under the presence of certain large cardinals).  ...  Assuming the existence of certain large cardinal numbers, we prove that for every projective filter F over the set of natural numbers, F-bases in Banach spaces have continuous coordinate functionals.  ...  We are indebted to Andrés Caicedo for drawing our attention to the Shelah-Woodin theorem and explaining to us various nuances concerning L(R).  ... 
arXiv:2005.04873v1 fatcat:o2g7aihdzvfjzfyll5psrxfyxu

Generic Large Cardinals and Systems of Filters

Giorgio Audrito, Silvia Steila
2017
Our reference text for large cardinals is [13] and for generic elementary embeddings is [8]. 1. (Filter property) For all a ∈ V λ , F a is a non trivial filter on P(a); (Compatibility) For all  ...  In this framework we investigate the topic of definability of generic large cardinals properties.  ...  We would like to thank Matteo Viale for his valuable suggestions, remarks and corrections; and for addressing us to the topic of generic large cardinals in the first place.  ... 
doi:10.7892/boris.112772 fatcat:zysnhyfvojdpzejbaqilx2zedu

Identifying High Cardinality Internet Hosts

J. Cao, Y. Jin, A. Chen, T. Bu, Z.-L. Zhang
2009 IEEE INFOCOM 2009 - The 28th Conference on Computer Communications  
Our approach consists of three components: 1) two-phase filtering for eliminating low cardinality hosts, 2) thresholded bitmap for counting cardinalities, and 3) bias correction.  ...  The main advantage of our approach is that it can filter out the majority of low cardinality hosts while preserving the hosts of interest, and hence minimize the memory resources wasted by tracking irrelevant  ...  A noticeably large number of hosts are observed to have large or extremely large cardinalities (also see Table I ).  ... 
doi:10.1109/infcom.2009.5061990 dblp:conf/infocom/CaoJCBZ09 fatcat:t57os3j7lbg2zibvtkjzkkjlvy

On the verge of inconsistency: Magidor cardinals and Magidor filters

Shimon Garti, Yair Hayut, Saharon Shelah
2017 Israel Journal of Mathematics  
We introduce a model-theoretic characterization of Magidor cardinals, from which we infer that Magidor filters are beyond ZFC-inconsistency  ...  We may conclude that Magidor filters can serve as a natural large cardinals axiom above ω-Jónsson cardinals.  ...  In some sense, Magidor filters continue the table of large cardinals beyond ω-Jónssonicity, since such a filter contains a measure-one set of ω-Jónsson cardinals.  ... 
doi:10.1007/s11856-017-1510-2 fatcat:h5erpo3bb5c7fcffp32grf7fim

A hierarchy of Ramsey-like cardinals

Peter Holy, Philipp Schlicht
2018 Fundamenta Mathematicae  
We introduce a hierarchy of large cardinals between weakly compact and measurable cardinals, that is closely related to the Ramsey-like cardinals introduced by Victoria Gitman in [Git11], and is based  ...  The aim of this paper is to locate the Ramsey-like cardinals studied by Gitman, and other well-known large cardinal notions, in this hierarchy.  ...  Introduction Ramsey cardinals are a very popular and well-studied large cardinal concept in modern set theory.  ... 
doi:10.4064/fm396-9-2017 fatcat:ezjrb4ylxbhuhijgipmq5e2ceq

A hierarchy of Ramsey-like cardinals [article]

Peter Holy, Philipp Schlicht
2017 arXiv   pre-print
We introduce a hierarchy of large cardinals between weakly compact and measurable cardinals, that is closely related to the Ramsey-like cardinals introduced by Victoria Gitman, and is based on certain  ...  The aim of this paper is to locate the Ramsey-like cardinals studied by Gitman, and other well-known large cardinal notions, in this hierarchy.  ...  Introduction Ramsey cardinals are a very popular and well-studied large cardinal concept in modern set theory.  ... 
arXiv:1710.10043v1 fatcat:24kyo3zxvncwddogw2qxanyc5y

A note on a question of Abe

Douglas Burke
2000 Fundamenta Mathematicae  
Assuming large cardinals, we show that every κ-complete filter can be generically extended to a V -ultrafilter with well-founded ultrapower. We then apply this to answer a question of Abe.  ...  It is possible that one can use large cardinals (and weakly precipitous filters) instead of precipitous filters.  ...  We can get by with much smaller large cardinals if all we want is α-weakly precipitous. Lemma 1.4. Assume F is a κ-complete filter and there is a measurable cardinal δ > | F|.  ... 
doi:10.4064/fm-163-1-95-98 fatcat:daibkhco2nfypj5p36wqlbq2va

Measurable cardinals and choiceless axioms [article]

Gabriel Goldberg
2021 arXiv   pre-print
We prove that if there is an elementary embedding from the universe to itself, then there is a proper class of measurable successor cardinals.  ...  Then for all cardinals κ, for all sufficiently large regular cardinals δ, the closed unbounded filter on δ is κ-complete.  ...  The following universality fact for fine filters, due to Kunen, allows us to conclude that under large cardinal hypotheses all sufficiently complete filters are wellfounded.  ... 
arXiv:2106.05916v3 fatcat:f2qq6lw4rjff3jh4vfnb33r5wa

Extraction of sparse spatial filters using Oscillating Search

Ibrahim Onaran, N. Firat Ince, Aviva Abosch, A. Enis Cetin
2012 2012 IEEE International Workshop on Machine Learning for Signal Processing  
In this paper, we apply the Oscillating Search (OS) method which fuses all these greedy search techniques to sparsify the CSP filters.  ...  Our results indicate that the OS method provides the lowest classification error rates with low cardinality levels where the complexity of the OS is around 20 times lower than the BE.  ...  The computational complexity is even higher when is large and the desired cardinality is small.  ... 
doi:10.1109/mlsp.2012.6349752 dblp:conf/mlsp/OnaranIAC12 fatcat:iv4n4fnebrgqjgu6xzenlludnq

Fast tag searching protocol for large-scale RFID systems

Yuanqing Zheng, Mo Li
2011 2011 19th IEEE International Conference on Network Protocols  
Since the cardinality of the products can be extremely large, collecting the tag information directly from each of those tags could be highly inefficient.  ...  The results demonstrate that the proposed tag searching protocol is highly efficient in terms of both time efficiency and transmission overhead, leading to good applicability and scalability for large-scale  ...  After filtering with , the cardinality of candidate tags will become much smaller than the original cardinality , in the cases that and is small.  ... 
doi:10.1109/icnp.2011.6089075 dblp:conf/icnp/ZhengL11 fatcat:r6zgmkuz4bbzzazb4uqgiw3oti

Square compactness and the filter extension property

David Buhagiar, Mirna Džamonja
2020 Fundamenta Mathematicae  
This is the first known improvement to the upper bound of strong compactness obtained in 1973 by Hajnal and Juhász.  ...  We show that the consistency strength of κ being 2 κ -square compact is at least weak compact and strictly less than indescribable.  ...  Mirna Džamonja thanks the University of Malta for their hospitality during summers of 2017, 2018 and 2019, when this work was done, and the Isaac Newton Institute in Cambridge, UK, and Simons Foundation  ... 
doi:10.4064/fm787-4-2020 fatcat:mq5y5mxu3bf7lajz4foihner2q

Fast Tag Searching Protocol for Large-Scale RFID Systems

Yuanqing Zheng, Mo Li
2013 IEEE/ACM Transactions on Networking  
Since the cardinality of the products can be extremely large, collecting the tag information directly from each of those tags could be highly inefficient.  ...  The results demonstrate that the proposed tag searching protocol is highly efficient in terms of both time efficiency and transmission overhead, leading to good applicability and scalability for large-scale  ...  After filtering with , the cardinality of candidate tags will become much smaller than the original cardinality , in the cases that and is small.  ... 
doi:10.1109/tnet.2012.2212454 fatcat:theuv6yjwfb3tj2mh2nw4wfcya

Variations of cub filter on $\mathcal{P}\sb \kappa\lambda$

Yo Matsubara
1988 Proceedings of the American Mathematical Society  
We make use of the partition property (a large cardinal hypothesis) to investigate the properties of these filters.  ...  In his 1973 paper, Jech extended the notion of cub and stationary sets to such sets in PKX and showed that many of their properties are preserved. We study variations of cub filters in this paper.  ...  Furthermore in this theory, those cardinals satisfying the large cardinal axioms are not necessarily large. For example, Solovay showed that Ni is a measurable cardinal under AD.  ... 
doi:10.1090/s0002-9939-1988-0934884-x fatcat:siha5bjdhna67hvr73w5yqncli
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