Kamsma, Mark (2023) Type space functors and interpretations in positive logic. Archive for Mathematical Logic, 62 (1-2). pp. 1-28. ISSN 0933-5846
Preview |
PDF (Kamsma2022_Article_TypeSpaceFunctorsAndInterpreta)
- Published Version
Available under License Creative Commons Attribution. Download (458kB) | Preview |
Abstract
We construct a 2-equivalence CohTheoryop≃TypeSpaceFunc. Here CohTheory is the 2-category of positive theories and TypeSpaceFunc is the 2-category of type space functors. We give a precise definition of interpretations for positive logic, which will be the 1-cells in CohTheory. The 2-cells are definable homomorphisms. The 2-equivalence restricts to a duality of categories, making precise the philosophy that a theory is ‘the same’ as the collection of its type spaces (i.e. its type space functor). In characterising those functors that arise as type space functors, we find that they are specific instances of (coherent) hyperdoctrines. This connects two different schools of thought on the logical structure of a theory. The key ingredient, the Deligne completeness theorem, arises from topos theory, where positive theories have been studied under the name of coherent theories.
Item Type: | Article |
---|---|
Uncontrolled Keywords: | bi-intepretation,coherent logic,interpretation,positive model theory,stone duality,type space,philosophy,logic ,/dk/atira/pure/subjectarea/asjc/1200/1211 |
Faculty \ School: | Faculty of Science > School of Mathematics |
UEA Research Groups: | Faculty of Science > Research Groups > Logic |
Related URLs: | |
Depositing User: | LivePure Connector |
Date Deposited: | 06 May 2022 03:59 |
Last Modified: | 09 Apr 2024 03:23 |
URI: | https://ueaeprints.uea.ac.uk/id/eprint/84907 |
DOI: | 10.1007/s00153-022-00825-7 |
Downloads
Downloads per month over past year
Actions (login required)
![]() |
View Item |