Virtual large cardinals
| Autor: | Victoria Gitman, Ralf Schindler |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Discrete mathematics
Hierarchy (mathematics) Logic 010102 general mathematics InformationSystems_DATABASEMANAGEMENT Mathematics::General Topology 06 humanities and the arts 0603 philosophy ethics and religion 01 natural sciences Mathematics::Logic Multiverse Large cardinal TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY 060302 philosophy Data_FILES 0101 mathematics MathematicsofComputing_DISCRETEMATHEMATICS Mathematics |
| Zdroj: | Annals of Pure and Applied Logic. 169:1317-1334 |
| ISSN: | 0168-0072 |
| Popis: | We introduce the concept of virtual large cardinals and apply it to obtain a hierarchy of new large cardinal notions between ineffable cardinals and 0 # . Given a large cardinal notion A characterized by the existence of elementary embeddings j : V α → V β satisfying some list of properties, we say that a cardinal is virtually A if the embeddings j : V α V → V β V exist in the generic multiverse of V. Unlike their ideological cousins generic large cardinals, virtual large cardinals are actual large cardinals that are compatible with V = L . We study virtual versions of extendible, n-huge, and rank-into-rank cardinals and determine where they fit into the large cardinal hierarchy. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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