Set Functors and Filters

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10294803" target="_blank" >RIV/00216208:11320/15:10294803 - isvavai.cz</a>
Result on the web
<a href="http://link.springer.com/article/10.1007/s10485-014-9367-6?no-access=true" target="_blank" >http://link.springer.com/article/10.1007/s10485-014-9367-6?no-access=true</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10485-014-9367-6" target="_blank" >10.1007/s10485-014-9367-6</a>

Result language
angličtina
Original language name
Set Functors and Filters
Original language description
For a filter F let cF(?) be the cardinality of the set of all filters isomorphic to F on a cardinal ?. We derive formulas for these functions similar to cardinal exponential formulas. We show that precise values of the function cF depends on the filter Fand also on the axioms of set theory. We apply these results to get a description of the function bF for a set functor F (bF(?) is the cardinality of F ? for a cardinal ?). We prove that the function bF depends on the functor F and on the axioms of settheory. For a partial cardinal function d, we find a sufficient condition for the existence of a set functor F with d(?)=bF(?) for all cardinals ? such that d(?) is defined. We prove that a functor F is finitary if and only if there exists a cardinal ? such that bF(?) is less or equal to ? for every cardinal ? greater or equal to ?. We prove an analogous necessary condition for small set functors and we prove that the precise characterization of small set functors depends on the axioms o
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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