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Indestructible weakly compact cardinals and the necessity of supercompactness for certain proof schemata [article]

Arthur W. Apter
1999 arXiv   pre-print
We show that if the weak compactness of a cardinal is made indestructible by means of any preparatory forcing of a certain general type, including any forcing naively resembling the Laver preparation,  ...  We then apply this theorem to show that the hypothesis of supercompactness is necessary for certain proof schemata.  ...  A key aspect of this construction involves preliminary forcing to transform κ into a supercompact limit of indestructible Ramsey cardinals and δ into a cardinal whose Ramseyness is indestructible by forcing  ... 
arXiv:math/9907046v1 fatcat:hjd7isfhhfdhrlh5ljzmyfq6ou

Page 7296 of Mathematical Reviews Vol. , Issue 2003j [page]

2003 Mathematical Reviews  
Benedikt Lowe (NL-AMST-LL; Amsterdam) 2003j:03068 03E55 03E35 Apter, Arthur W. (1-CUNY2; New York, NY) Aspects of strong compactness, measurability, and indestructibility. (English summary) Arch.  ...  «, and «2, both the first two strongly compact and the first two measurable cardinals and such that K\’s strong compactness and «2’s measurability are indestructible for «\-directed and « -directed closed  ... 

Page 809 of Mathematical Reviews Vol. , Issue 2003B [page]

2003 Mathematical Reviews  
Apter, “Aspects of strong compactness, measurability, and indestructibility”, Arch. Math.  ...  From the text: “Laver indestructibility [R. Laver, Israel J. Math. 29 (1978), no. 4, 385-388; MR 57 #12226] in the context of strong compactness has now been the subject of several papers.  ... 

Small forcing makes any cardinal superdestructible

Joel David Hamkins
1998 Journal of Symbolic Logic (JSL)  
In fact, after small forcing, any cardinal κ becomes superdestructible—any further <κ-closed forcing which adds a subset to κ will destroy the measurability, even the weak compactness, of κ.  ...  Small forcing always ruins the indestructibility of an indestructible supercompact cardinal.  ...  and weak compactness of κ.  ... 
doi:10.2307/2586586 fatcat:khmskes67zbi5g7zmhr5rrng2u

Inner models with large cardinal features usually obtained by forcing

Arthur W. Apter, Victoria Gitman, Joel David Hamkins
2011 Archive for Mathematical Logic  
strong compactness and supercompactness.  ...  Under the same hypothesis, there is an inner model with level by level equivalence between strong compactness and supercompactness, and indeed, another in which there is level by level inequivalence between  ...  between strong compactness and supercompactness hold".  ... 
doi:10.1007/s00153-011-0264-5 fatcat:ufdzoyy47ve37c5ka4uwfzlzzq

Inner models with large cardinal features usually obtained by forcing [article]

Arthur Apter and Victoria Gitman and Joel David Hamkins
2011 arXiv   pre-print
strong compactness and supercompactness.  ...  Under the same hypothesis, there is an inner model with level by level equivalence between strong compactness and supercompactness, and indeed, another in which there is level by level inequivalence between  ...  The research of each of the authors has been supported in part by research grants from the CUNY Research Foundation.  ... 
arXiv:1111.0856v1 fatcat:tpoacnv27ndgbi6sqigtxsmlci

SPM Bulletin 25 [article]

Boaz Tsaban
2008 arXiv   pre-print
Indestructible colourings and rainbow Ramsey theorems; 8. Products of Borel subgroups; 9. Selection theorems and treeability; 10.  ...  Combinatorial and model-theoretical principles related to regularity of ultrafilters and compactness of topological spaces, I; 2. Frechet-Urysohn fans in free topological groups; 3.  ...  Indestructible colourings and rainbow Ramsey theorems.  ... 
arXiv:0808.2803v1 fatcat:hest3h6qhngppn24jrqa2wffwy

Combined Maximality Principles up to large cardinals

Gunter Fuchs
2009 Journal of Symbolic Logic (JSL)  
So the question is whether it is consistent to have this principle at unboundedly many regular cardinals or at every regular cardinal below some large cardinal κ (instead of ∞), and if so, how strong it  ...  Remark 2.12 shows an interesting aspect of the next lemma, because it provides a new way of producing an indestructibly weakly compact cardinal, other than using the Laver preparation to make a supercompact  ...  If κ is measurable, U is a normal ultrafilter on κ and the set of κ < κ such that MP <κ−closed (Hκ ∪ {κ}) holds has U -measure 1, then the set of indestructibly weakly compact cardinals below κ has U -  ... 
doi:10.2178/jsl/1245158097 fatcat:ucz44d5hx5aphmesbujedvxzwu

Unprepared Indestructibility [article]

Andrew Brooke-Taylor
2012 arXiv   pre-print
This article is based on the talk of the same name which I gave at the "Aspects of Descriptive Set Theory" RIMS Symposium in Kyoto in October 2011; it is essentially just a survey of my article "Indestructibility  ...  In particular, I present (with a sketch of the proof) a forcing indestructibility theorem for the large cardinal axiom Vopenka's Principle.  ...  of a "compactness" flavour.  ... 
arXiv:1202.5836v1 fatcat:r3zpetkemvftlpi444imnpqvfq

Laver and set theory

Akihiro Kanamori
2016 Archive for Mathematical Logic  
In this commemorative article, the work of Richard Laver is surveyed in its full range and extent.  ...  Doctoral students of Richard Laver Stephen Grantham, An analysis of Galvin In addition to having these doctoral students at Boulder, Laver was on the thesis committees of, among many:  ...  reals can have strong measure zero, and so, that no uncountable Borel set can have strong measure zero.  ... 
doi:10.1007/s00153-015-0462-7 fatcat:5ziwvh27arbprhsdlmku4f2npe

Maximal Blaschke Products [article]

Daniela Kraus, Oliver Roth
2013 arXiv   pre-print
We show that the extremal function is essentially unique and always an indestructible Blaschke product.  ...  This result extends the Nehari--Schwarz Lemma and leads to a new class of Blaschke products called maximal Blaschke products.  ...  We wish to thank an anonymous referee for carefully reading the paper and providing us with a number of suggestions.  ... 
arXiv:1303.6769v2 fatcat:egsck6djbvfgbcvf6accmihqeu

Dust-aggregate impact into granular matter: A systematic study of the influence of projectile velocity and size on crater formation and grain ejection

María Belén Planes, Emmanuel N. Millán, Herbert M. Urbassek, Eduardo M. Bringa
2017 Astronomy and Astrophysics  
The crater walls are compacted by the impact within a zone of a size comparable to the crater radius.  ...  Granular-mechanics simulations are used to study the outcome of dust-aggregate impacts. The granular bed and the aggregates are composed of silica grains and have filling factor 0.36. Results.  ...  We thank Christian Ringl and Nina Gunkelmann for help with the setup of the simulation target and for discussions.  ... 
doi:10.1051/0004-6361/201730954 fatcat:guqel3rdlnctvmda457gw7erke

Making all cardinals almost Ramsey

Arthur W. Apter, Peter Koepke
2008 Archive for Mathematical Logic  
supported by PSC-CUNY grants and CUNY Abstract We examine combinatorial aspects and consistency strength properties of almost Ramsey cardinals.  ...  percompact Radin forcing, Radin sequence of measures, symmetric inner model. ‡ We wish to thank Ralf Schindler for his insightful comments concerning Theorem 2. § The first author's research was partially  ...  Due to the strong indestructibility of almost Ramsey cardinals, the large cardinal hypotheses in the ground model can be taken considerably weaker than in a similar construction found in [5] .  ... 
doi:10.1007/s00153-008-0107-1 fatcat:5pjpbz5czvcwthbjnuzt2kuli4

Menas' result is best possible [article]

Arthur Apter, Saharon Shelah
1995 arXiv   pre-print
Generalizing some earlier techniques due to the second author, we show that Menas' theorem which states that the least cardinal kappa which is a measurable limit of supercompact or strongly compact cardinals  ...  Using these same techniques, we also extend and give a new proof of a theorem of Woodin and extend and give a new proof of an unpublished theorem due to the first author.  ...  We mention that we are assuming complete familiarity with the notions of measurability, strong compactness, and supercompactness.  ... 
arXiv:math/9512226v1 fatcat:jvb3w5n73fa7net5dyr2ewxt4u

Human Personality and Charaka's Theory of Dhatus

Dr. Biswajit Satpathy
2022 International Journal of Research Publication and Reviews  
Charaka, one of the great physicians of Ayurvedic medicine, methodically observed the human behaviours and temperaments.  ...  The theory of Dhatus (Tissues) is a typical element in Ayurvedic medical science. The human body contains eight main substances; known as Dhatus that give support and strength to our body.  ...  Such individual are loved by women, they are strong and endowed with happiness, power, health, wealth, honor and children 11 Shukra Sara person is known to possess unctuous, compact and white bones,  ... 
doi:10.55248/gengpi.2022.3.9.7 fatcat:3shxd2i54vaexblnic3tvcnb3e
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