M. Forti and F. Honsell. "Models of self-descriptive set theories." Partial Differential Equations and the Calculus of Variations, Vol. 1, ed. by F. Colombini, A. Marino, L. Modica and S. Spagnolo, Birkhauser, Boston, 1989. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
On Transition Systems and Non-Well-Founded Sets - Lazic, al. (1996) (1 citation) (Correct)
....presence of AFA. Non well founded set theory has been worked on long before [Acz 88] In particular, AFA was probably rst introduced as X 1 by Forti and Honsell in [FH 83] which investigates a number of axioms derived from a Free Construction Principle. In the subsequent papers (especially in [FH 89] and [FH 92] they study structures which correspond to our canonical transition systems at regular cardinal heights (and for a singleton alphabet) They regard them primarily as quotients of a universe satisfying AFA. Working in set theory with AFA, Aczel and Mendler obtain a Terminal Coalgebra ....
.... obtain a Terminal Coalgebra Theorem (see Chapter 7 of [Acz 88] and [AczM 89] which can be used to obtain spaces for semantics of process algebras based on the idea that [ P ] fh; P 0 ] i j P P 0 g (see Chapter 8 of [Acz 88] and e.g. RT 93] By generalising the structures from [FH 89] and [FH 92] Forti, Honsell and Lenisa arrive at hyperuniverses, which are models of a strong Comprehension Scheme with topological structure, and can be similarly used for denotational semantics see [FHL 94] 2 Transition systems, morphisms and bisimulations We work within ZFC , i.e. ....
[Article contains additional citation context not shown here]
Forti, M. and Honsell, F., Models of self-descriptive set theories, in Partial di erential equations and the calculus of variations, Volume 1 | Essays in honor of Ennio De Giorgi (Colombini, F. et al., eds.), 473-518, Birkhauser, 1989.
Processes and Hyperuniverses - Marco Forti (1994) (7 citations) Self-citation (Forti Honsell) (Correct)
....set a. These theories have a very limited self descriptive power, in that they do not even allow the existence of a universal set. Comprehensive Theories of Sets were investigated among others by Quine (30 s) Church (50 s) Malitz (70 s) More recently Forti, Hinnion, Honsell and Weydert ([7, 9, 14]) considered a very strong version of comprehension consistent with extensionality, namely the Generalized Positive Comprehension Principle: GPC fx j OE(x)g is a set, if OE is a Generalized Positive Formula. 3 The Comprehension Schema GPC is quite powerful (see [7] Inter alia, it allows the ....
.... yg; x [ y; x y; x Theta y; x ffi y, S x; T x; dom(x) cod(x) x Gamma1 ; P(x) x) fy j y x 6= g; b x(y) fz j 9w 2 y: w; z) 2 xg; F(x) fy j x 2 yg; x y = f(u; v; w) j (u; v) 2 x (u; w) 2 yg: Hyperuniverses are models of comprehensive theories of sets even stronger than GPC [7, 9, 14]. The following definition of hyperuniverse generalizes of the notion introduced in [10] to a Set Theory with Urelements (i.e. atoms) Definition 1. Let N be a transitive set and let U be the set of Urelements of N . Then N is a hyperuniverse if the following conditions hold: 4 i) the ....
[Article contains additional citation context not shown here]
M. Forti, F. Honsell, Models of self-descriptive Set Theories, in Partial Differential Equations and the Calculus of Variations, Essays in Honor of E. De Giorgi (F. Colombini et al. editors), Birkhauser, Boston 1989, 473--518.
Axiomatic Characterizations of Hyperuniverses and Applications - Forti, Honsell Self-citation (Forti Honsell) (Correct)
....at the 11 th Summer Conference on General Topology and Applications August 1995, Portland, Maine. Introduction Natural frameworks for dicussing Selfreference and other circular phenomena are extremely useful in areas such as the Foundations of Mathematics and Computer Science (see e.g. [2, 8, 11, 20, 24]) or the Semantics of Natural and Programming Languages (see e.g. 1, 3, 4, 15, 19, 21, 22] Hyperuniverses can play the role of such frameworks. From the foundational point of view, hyperuniverses are transitive models of non standard set theories which do not abide by the limitation of size ....
....22] Hyperuniverses can play the role of such frameworks. From the foundational point of view, hyperuniverses are transitive models of non standard set theories which do not abide by the limitation of size principle and hence they provide comprehensive but intuitive universes of sets (see [8, 11, 12, 13]) Many classes having the size of the universe, such as those necessary for an adequate self description, are sets of the hyperuniverse; moreover it is closed under many basic set theoretic operations. From the semantical point of view, hyperuniverses provide a uniform setting for solving many ....
[Article contains additional citation context not shown here]
M.Forti, F.Honsell, Models of Selfdescriptive Set Theories, in Partial Differential Equations and the Calculus of Variations, Essays in Honor of Ennio De Giorgi, I (F.Colombini et al. eds.), Birkhauser, Boston 1989, 473-518.
Linear Set Theory - Shirahata (1995) (3 citations) (Correct)
No context found.
M. Forti and F. Honsell. "Models of self-descriptive set theories." Partial Differential Equations and the Calculus of Variations, Vol. 1, ed. by F. Colombini, A. Marino, L. Modica and S. Spagnolo, Birkhauser, Boston, 1989.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC