DSpace at School of Computing, NUS: Item 1900.100/3055

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Title:	Implementing Fragments of ZFC within an r.e. Universe
Authors:	MARTIN, Eric PONG, Wai Yan STEPHAN, Frank
Issue Date:	30-Jun-2009
Series/Report no.:	;TRE6/09
Abstract:	Rabin showed that there is no r.e. model of the axioms of Zermelo and Fraenkel of set theory. In the present work, it is investigated to which extent natural models of a sufficiently rich fragment of set theory exist. Such models, called Friedberg models in the present work, are built as a class of subsets of the natural numbers, together with the element-relation given as x is in y if and only if x is in the set y-th r.e. set from a given Friedberg numbering of all r.e. sets of natural numbers. The y-th member of this numbering is then considered to be a set in the given model iff the downward closure of the induced element-ordering from y is well-founded. For each axiom and basic property of set theory, it is shown whether or not that axiom or property holds in such a model. Comprehension and replacement need to be properly adapted, as not all functions and objects definable using first-order logic exist in the model. The validity of the power set axiom, in an adequate formulation, ...
URI:	http://hdl.handle.net/1900.100/3055
Appears in Collections:	Technical Reports

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