DS-2011-05: Keskinen, Lauri (2011) Characterizing All Models in Infinite Cardinalities. Doctoral thesis, University of Amsterdam.
![[thumbnail of Full Text]](https://eprints.illc.uva.nl/style/images/fileicons/text.png) |
Text (Full Text)
DS-2011-05.text.pdf Download (613kB) |
|
Text (Samenvatting)
DS-2011-05.samenvatting.txt Download (1kB) |
Abstract
Fix a cardinal kappa. We can ask the question what kind of a logic L is
needed to characterize all models of cardinality kappa (in a finite
vocabulary) up to isomorphism by their L-theories. In other words: for
which logics L it is true that if any models A and B satisfy the same
L-theory then they are isomorphic.
It is always possible to characterize models of cardinality kappa by their
L_{kappa ^+ ,kappa ^+ }-theories, but we are interested in finding a
``small" logic L, i.e. the sentences of L are hereditarily smaller than
kappa. For any cardinal kappa it is independent of ZFC whether any such
small definable logic L exists. If it exists it can be second order logic
for kappa=omega and fourth order logic or certain infinitary second order
logic L^2 _{kappa ,omega } for uncountable kappa. All models of cardinality
kappa can always be characterized by their theories in a small logic with
generalized quantifiers, but the logic may be not definable in the language
of set theory.
| Item Type: | Thesis (Doctoral) |
|---|---|
| Report Nr: | DS-2011-05 |
| Series Name: | ILLC Dissertation (DS) Series |
| Year: | 2011 |
| Subjects: | Language Logic |
| Depositing User: | Dr Marco Vervoort |
| Date Deposited: | 14 Jun 2022 15:16 |
| Last Modified: | 14 Jun 2022 15:16 |
| URI: | https://eprints.illc.uva.nl/id/eprint/2100 |
Actions (login required)
 |
View Item |
