Duality and definability in first order logic
We develop a duality theory for small Boolean pretoposes in which the dual of the [italic capital]T is the groupoid of models of a Boolean pretopos [italic capital]T equipped with additional structure derived from ultraproducts. The duality theorem states that any small Boolean pretopos is canonically equivalent to its double dual. We use a strong version of the duality theorem to prove the so-called descent theorem for Boolean pretoposes which says that category of descent data derived from a …
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- Full title :Duality and definability in first order logic / Michael Makkai.
Summary
We develop a duality theory for small Boolean pretoposes in which the dual of the [italic capital]T is the groupoid of models of a Boolean pretopos [italic capital]T equipped with additional structure derived from ultraproducts. The duality theorem states that any small Boolean pretopos is canonically equivalent to its double dual. We use a strong version of the duality theorem to prove the so-called descent theorem for Boolean pretoposes which says that category of descent data derived from a conservative pretopos morphism between Boolean pretoposes is canonically equivalent to the domain-pretopos. The descent theorem contains the Beth definability theorem for classical first order logic. Moreover, it gives, via the standard translation from the language of categories to symbolic logic, a new definability theorem for classical first order logic concerning set-valued functors on models, expressible in purely syntactical (arithmetical) terms.
Read More ↓Edition Statements
- Publication Date:©1993.
Publication Statements
- Publisher(s):American mathematical Society
- Place of Publication:Providence, R.I
- Language:eng
- Publication Date:©1993.
Notes
"September 1993, volume 105, number 503 (fourth of 6 numbers)."
The Physical Object
- Description:x, 106 pages : : illustrations ; : 26 cm.
Edition Identifiers
- ISBN:0821825658, 9780821825655
- oclc:ocm28213441
- LC Classification:QA3
- Dewey Decimal:510 s
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