منابع مشابه
Classification of non-well-founded sets and an application
In set theory, the foundation axiom (or regularity)(F) says that the relation ∈ is well-founded, that is, there is no infinite descending ∈-sequence : · · · ∈ x 2 ∈ x 1 ∈ x 0. If we identify ∈ in a set with ← in a graph, the set is identified with a graph. The set 1 is 1 = {φ}, that is, φ ∈ 1. It corresponds to a graph x 1 ← x 0 with nodes x 0 , x 1. In terms of graphs and nodes, the well-found...
متن کاملA non-well-founded primitive recursive tree provably well-founded for co-r.e. sets
We construct by diagonalization a non-well-founded primitive recursive tree, which is well-founded for co-r.e. sets, provable in Σ01-IND. It follows that the supremum of order-types of primitive recursive wellorderings, whose well-foundedness on co-r.e. sets is provable in Σ01-IND, equals the limit of all recursive ordinals ω 1 . This work contributes to the investigation of replacing the quant...
متن کاملA Cook's Tour of the Finitary Non-Well-Founded Sets
It is a great pleasure to contribute this paper to a birthday volume for Dov. Dov and I arrived at imperial College at around the same time, and soon he, Tom Maibaum and I were embarked on a joint project, the Handbook of Logic in Computer Science. We obtained a generous advance from Oxford University Press, and a grant from the Alvey Programme, which allowed us to develop the Handbook in a rat...
متن کاملNon-Well-Founded Sets Modeled as Ideal Fixed Points
Motivated by ideas from the study of abstract data types, we show how to interpret non-well-founded sets as tixed points of continuous transformations of an initial continuous algebra. We conisder a preordered structure closely related to the set HF of well-founded, hereditarily finite sets. By taking its ideal completion, we obtain an initial continuous algebra in which we are able to solve al...
متن کاملWell- and Non-Well-Founded Fregean Extensions
George Boolos has described an interpretation of a fragment of ZFC in a consistent second-order theory whose only axiom is a modification of Frege’s inconsistent Axiom V. We build on Boolos’s interpretation and study the models of a variety of such theories obtained by amending Axiom V in the spirit of the principle of limitation of size. After providing a complete structural description of all...
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ژورنال
عنوان ژورنال: MLQ
سال: 2003
ISSN: 0942-5616,1521-3870
DOI: 10.1002/malq.200310018