Sheaves and Logic

Sheaves and Logic

[categories]

Date: Thu, 4 Dec 1997 12:17:39 -0300 (EST)
From: Regivan Hugo Nunes Santiago <rhns@di.ufpe.br>


	Dear friends, I am a PhD Student in Computer Science at 
Departamento de Informatica, UFPE, Brazil, and I need to study the
theory of sheaves and its conexion with logic. However I am finding some
dificulties concerning matterials who have an intuitive explanation of the
subject. I am reading Michael Fourman and D. Scott's Sheaves and Logic
paper. It would be helpful if you could give me an intuition
about the following questions:

	Is there any intuition about the notions of global and local
objects? 

	What is the connection between global and local objects, and, for
example, partial and total functions?

	Is there any intuition about the existence predicate
E:|A|->\omega?

	What is a singleton?

	In the paper "Identity and Existence", in the same proceedings,
Scott formalized the notion of partial objects (e.g.partial functions).
If we are modelling the standard intuitionistic logic,
the local objects makes sense? Let me explain what I want to get.
Is sheaves an adequate model for intuitionistic logic just when we
want to formalize the notion of partial objects? And if we are working
with standard intuitionistic logic, does the category of structure
generated by a first order theory contain strutures with, for example, 
partial functions?

	Is there any intuitive written material about the subject?


					My best regards
					    Regivan
---------------------------
Regivan H. N. Santiago
http://www.di.ufpe.br/~rhns
Recife-Pernambuco/Brazil
---------------------------