1 Introduction 

1 






2 Basic Definitions and Formalizations 

6 



2.1 Basic Definitions 

6 
2.2 ModelTheoretic Observations 

13 
2.3 Formalizations 

18 
2.4 Main Theorems 

27 



3 A Σ_{1}−Completeness Theorem 

31 



3.1 Base Theory 

33 
3.2 Skolemization of xÎI 

36 
3.3 The Proof 

42 



4 A Proper Subtheory of IΔ_{0}+Ω
_{1} 

49 



4.1 Skolemizing IΔ_{0}+Ω 

50 
4.2 The Proof 

55 



5 Relations to Earlier Results 

66 



5.1 A Solution to Adamowicz & Zbierski's Problem 

66 
5.2 A Generalization of Adamowicz's Theorem 

68 
5.2.1 Skolemizing
xÎlog^{3} 

70 
5.2.2 The Proof 

72 



References 

75 
Index 

78 