ABSTRACT:
A Paris model M is a model of set theory all of whose ordinal are first order definable in M. Jeffrey Paris (1973) initiate the study these models and showed that (1) every consistent extension T of ZF has a Paris model, and (2) for complete extentions T, T has a unique Paris model uo to isomorphism iff T proves V=OD. In this thesis we study
including the following results.
(1) If T is a consistent completion of ZF + V = OD then T has continuum-many countable nonisomorphic
(2) Every countable models of ZFC has a
(3) If there is an uncountable well-founded model of ZFC, then for every infinit cardinal k there is a
(4) For a model M of ZF, If M is a prime model then M is a