Inverse topological systems and compactness in abstract model theory

Journal of Symbolic Logic 51 (3):785-794 (1986)
Given an abstract logic L = L(Q i ) i ∈ I generated by a set of quantifiers Q i , one can construct for each type τ a topological space S τ exactly as one constructs the Stone space for τ in first-order logic. Letting T be an arbitrary directed set of types, the set $S_T = \{(S_\tau, \pi^\tau_\sigma)\mid\sigma, \tau \in T, \sigma \subset \tau\}$ is an inverse topological system whose bonding mappings π τ σ are naturally determined by the reduct operation on structures. We relate the compactness of L to the topological properties of S T . For example, if I is countable then L is compact iff for every τ each clopen subset of S τ is of finite type and S τ is homeomorphic to $\underset{lim}S_T$ , where T is the set of finite subtypes of τ. We finally apply our results to concrete logics
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2307/2274032
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 24,463
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA
K. Jon Barwise (1974). Axioms for Abstract Model Theory. Annals of Mathematical Logic 7 (2-3):221-265.
Daniele Mundici (1981). Applications of Many-Sorted Robinson Consistency Theorem. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 27 (11-12):181-188.

View all 6 references / Add more references

Citations of this work BETA
Xavier Caicedo (1993). Compactness and Normality in Abstract Logics. Annals of Pure and Applied Logic 59 (1):33-43.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

10 ( #409,248 of 1,925,521 )

Recent downloads (6 months)

1 ( #418,235 of 1,925,521 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.