Admissible Sets and Structures

Barwise, Jon

doi:10.1007/978-3-662-11035-5

Cited by 615 publications

(371 citation statements)

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“…All atoms of an organization shall be elements of an universal admissible set U. Using admissible sets allow us to consider certain sets as atoms without messing the organization construct [5, 13]. These sets differ in concept and formalism from the set in clause 2 of Definition 2.1.…”

Section: Biological Organization: a Minimalist Snapshotmentioning

confidence: 99%

Biological Organization, Biological Information, and Knowledge

Kritz¹

2014

Preprint

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A concept of information designed to handle information conveyed by organizations is introduced. This concept of information may be used at all biological scales: from molecular and intracellular to multi-cellular organisms and human beings, and further on to collectivities, societies and culture. In this short account, two ground concepts necessary for developing the definition will also be introduced: whole-part graphs, a model for biological organization, and synexions, their immersion into space-time. This definition of information formalizes perception, observers and interpretation; allowing for considering information-exchange as a basic form of biological interaction. Some of its elements will be clarified by arguing and explaining why the immersion of whole-part graphs in (the physical) space-time is needed.

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Section: Biological Organization: a Minimalist Snapshotmentioning

confidence: 99%

Biological Organization, Biological Information, and Knowledge

Kritz¹

2014

Preprint

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“…It is well-known (see, for example, Barwise [4]) that there are ∆ 0 formulas Rel (a) and Fun(a) of our basic language L, stating that the set a is a binary relation and function, respectively, in the typical set-theoretic sense. It can also be expressed in ∆ 0 form that a is a relation with domain b, abbreviated as Dom(a) = b, and that a is a relation with range b, abbreviated as Ran(a) = b.…”

Section: Ifmentioning

confidence: 99%

On Feferman’s operational set theory OST

Jäger

2007

Annals of Pure and Applied Logic

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“…Mathematical logicians also developed generalized computability theory over abstract sets (of sets of sets, etc.) in the form of admissible set theory (Barwise, 1975). In computer science, a set theoretic programming language SETL was created (quite naturally, for the case of finite sets only).…”

Section: Introductionmentioning

confidence: 99%

HYPERSET/WEB-LIKE DATABASES AND THE EXPERIMENTAL IMPLEMENTATION OF THE QUERY LANGUAGE DELTA - Current State of Affairs

Molyneux

Sazonov

2007

Proceedings of the Second International Conference on Software and Data Technologies

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Abstract:The hyperset approach to WEB-like or semistructured databases is outlined. WDB is presented either (i) as a finite edge-labelled graph or, equivalently, (ii) as system of (hyper)set equations or (iii) in a special XML-WDB format convenient both for distributed WDB and for including arbitrary XML elements in this framework. The current state of affairs on experimental implementation of a query language ∆ (Delta) to such databases-the main result of this paper-is described, with consideration of further implementation work to be done.

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Admissible Sets and Structures

Cited by 615 publications

References 0 publications

Biological Organization, Biological Information, and Knowledge

Biological Organization, Biological Information, and Knowledge

On Feferman’s operational set theory OST

HYPERSET/WEB-LIKE DATABASES AND THE EXPERIMENTAL IMPLEMENTATION OF THE QUERY LANGUAGE DELTA - Current State of Affairs

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