Duality and Definability in First Order Logic is popular PDF and ePub book, written by Michael Makkai in 1993, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Duality and Definability in First Order Logic can be Read Online from any device for your convenience.
Duality and Definability in First Order Logic Book PDF 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.
Detail Book of Duality and Definability in First Order Logic PDF
- Author : Michael Makkai
- Release : 30 September 1993
- Publisher : American Mathematical Soc.
- ISBN : 9780821825655
- Genre : Mathematics
- Total Page : 122 pages
- Language : English
- PDF File Size : 9,5 Mb
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