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 Paris models, including the following results. (1) If T is a consistent completion of ZF + V = OD then T has continuum-many countable nonisomorphic Paris models. (2) Every countable models of ZFC has a paris generic extention. (3) If there is an uncountable well-founded model of ZFC , then for every infinit cardinal k there is a Paris model of ZF of cardinality k which has a nontrivial automorphism. (4) For a model M of ZF , If M is a prime model then M is a paris model and satisfies AC , and If M is a paris model and satisfies AC then M is a minimal model. Moreover, Niether implication reverses assuming Con( ZF ).
