Please use this identifier to cite or link to this item:
https://doi.org/10.1093/logcom/exx030
Title: | Implementing fragments of ZFC within an r.e. Universe | Authors: | Martin E. Stephan F. |
Keywords: | axioms of Zermelo Fraenkel set theory (ZFC) Friedberg numbering Recursively enumerable model |
Issue Date: | 2018 | Publisher: | Oxford University Press | Citation: | Martin E., Stephan F. (2018). Implementing fragments of ZFC within an r.e. Universe. Journal of Logic and Computation 28 (1) : 30. ScholarBank@NUS Repository. https://doi.org/10.1093/logcom/exx030 | Abstract: | The present work addresses the question: to what extent do natural models of a sufficiently rich fragment of set theory exist? Such models, here called Friedberg models, are built as a class of sets of natural numbers together with the element-relation "x is in y" given by xin Ay, where A0, A1, A2, is a Friedberg numbering of all r.e. sets of natural numbers. A member A-x of this numbering is considered to be a set in the given model iff the transitive closure of the induced membership relation starting from x is well-founded. Furthermore, for all k, the set Bk = x: Ax has size k must be recursive. It will be examined whether the axioms of set theory and some basic set-theoretic properties hold in such a model. Because they do not hold in full generality, comprehension and replacement need to be properly adapted. The validity of the axiom of power set depends on the Friedberg model under consideration. The other axioms hold in every Friedberg model. | Source Title: | Journal of Logic and Computation | URI: | https://scholarbank.nus.edu.sg/handle/10635/177524 | ISSN: | 0955-792X | DOI: | 10.1093/logcom/exx030 |
Appears in Collections: | Staff Publications Elements |
Show full item record
Files in This Item:
File | Description | Size | Format | Access Settings | Version | |
---|---|---|---|---|---|---|
reset.pdf | 367.16 kB | Adobe PDF | OPEN | Post-print | View/Download |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.