Replacement Schema.
Hi all,
Can the following theorum schema be proved in ZFC?
if P is any predicate in two variables,then all closures of
(AxEcAy(yec<->P(x,y)))->AaEbAy(yeb<->Exea(P(x,y))).
are theorums in ZFC.
Zuhair
.
Relevant Pages
- Re: Simplifying M theories.
... Perhaps you mean the axioms relativized to the predicate 'set'. ... universe, so that S maps predicates of RA to subsets of R. ... ZFC Extensionality: ... (sci.logic) - Re: Lets you & him fight
... the first-order language of set theory a satisfaction predicate, ... theory, call it ZFC*, is not conservative over ZFC, it has much ... Thus, given we accept an inaccessible or something beyond ZFC, we can recognize the resulting theory as comprising exactly the principles that are acceptable on basis of acceptance of ZFC, similarly as RA_Gamma_0 - predicative analysis - comprises exactly the principles acceptable on basis of acceptance of the totality of natural numbers as determinate - so that arithmetical truth is a legitimate notion - and induction in the informal sense. ... (sci.logic) - Re: The set of All sets
... >No axioms of ZFC mention 'set'. ... One can define the predicate 'is a set' ... Herman Rubin, Department of Statistics, Purdue University ... (sci.math) - Re: Why cant such an example be given?
... No predicate can be proven to exist in ZFC, ... i am fully aware that ZFC is not a second order language ... i.e. it can be proven that thereExists S_P_O ... (sci.math) - Re: Small set Theory:final version.
... Extensionality: As in ZFC. ... Regularity: As in ZFC. ... nor it is biconditioned to a predicate in one variable that use x. ... "Radicals are interesting because they were considered 'radical' by ... (sci.math) |
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