A Spector-Gandy theorem for cPCd(A) classes

Journal of Symbolic Logic 57 (2):478 - 500 (1992)
Let U be an admissible structure. A cPCd(U) class is the class of all models of a sentence of the form $\neg\exists\bar{K} \bigwedge \Phi$ , where K̄ is an U-r.e. set of relation symbols and φ is an U-r.e. set of formulas of L∞ω that are in U. The main theorem is a generalization of the following: Let U be a pure countable resolvable admissible structure such that U is not Σ-elementarily embedded in HYP(U). Then a class K of countable structures whose universes are sets of urelements is a cPCd(U) class if and only if for some Σ formula σ (with parameters from U), M is in K if and only if M is a countable structure with universe a set of urelements and $(\mathrm{HYP}_\mathfrak{U}(\mathfrak{M}), \mathfrak{U}, \mathfrak{M}) \models \sigma$ , where HYPU(M), the smallest admissible set above M relative to U, is a generalization of HYP to structures with similarity type Σ over U that is defined in this article. Here we just note that when Lα is admissible, HYPLα(M) is Lβ(M) for the least β ≥ α such that Lβ(M) is admissible, and so, in particular, that HYPHF(M) is just HYP(M) in the usual sense when M has a finite similarity type. The definition of HYPU(M) is most naturally formulated using Adamson's notion of a +-admissible structure (1978). We prove a generalization from admissible to +-admissible structures of the well-known truncation lemma. That generalization is a key theorem applied in the proof of the generalized Spector-Gandy theorem
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2307/2275283
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 32,564
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

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles
Σ1-Separation.Fred G. Abramson - 1979 - Journal of Symbolic Logic 44 (3):374 - 382.
Countable Structures, Ehrenfeucht Strategies, and Wadge Reductions.Tom Linton - 1991 - Journal of Symbolic Logic 56 (4):1325-1348.
Les Automorphismes d'Un Ensemble Fortement Minimal.Daniel Lascar - 1992 - Journal of Symbolic Logic 57 (1):238-251.
∑1 Definitions with Parameters.T. A. Slaman - 1986 - Journal of Symbolic Logic 51 (2):453 - 461.
HC of an Admissible Set.Sy D. Friedman - 1979 - Journal of Symbolic Logic 44 (1):95-102.
The Pure Part of HYP(M).Mark Nadel & Jonathan Stavi - 1977 - Journal of Symbolic Logic 42 (1):33-46.
Added to PP index

Total downloads
397 ( #8,191 of 2,235,792 )

Recent downloads (6 months)
3 ( #193,244 of 2,235,792 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature