Identity crises and strong compactness
✍ Scribed by Arthur W. Apter; James Cummings
- Publisher
- Springer
- Year
- 2001
- Tongue
- English
- Weight
- 137 KB
- Volume
- 40
- Category
- Article
- ISSN
- 0933-5846
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
It is proved that ff strongly compact cardinals ale consistent, then it is consistent that the fb~t such cardinal is the first measurable. On the othat hand, if it is consistent to asmlne the existence of supcrcompact cardinal, then it is consistent to assume that it is the t~trst strongly compact c
## Abstract For any ordinal __δ__, let __λ~δ~__ be the least inaccessible cardinal above __δ__. We force and construct a model in which the least supercompact cardinal __κ__ is indestructible under __κ__‐directed closed forcing and in which every measurable cardinal __δ__ < __κ__ is < __λ~δ~__ stro
## Abstract We construct a model in which the strongly compact cardinals can be non‐trivially characterized via the statement “__κ__ is strongly compact iff __κ__ is a measurable limit of strong cardinals”. If our ground model contains large enough cardinals, there will be supercompact cardinals in
## Abstract We force and construct models in which there are non‐supercompact strongly compact cardinals which aren't measurable limits of strongly compact cardinals and in which level by level equivalence between strong compactness and supercompactness holds non‐trivially except at strongly compac