Skolemization is a well-known method for removing existential quantifiers from a logical formula. Although it always yields a satisfiability-preserving transformation step, classical Skolemization in general does not preserve the logical meaning of a source formula. Based on a general framework for generating and extending logical structures on specialization systems, we develop in this paper a theory for extending a space of logical formulas by incorporation of function variables and show how meaning-preserving Skolemization can be achieved in an obtained extended space. A procedure for converting a logical formula into an equivalent one in a conjunctive normal form on the extended space is described. This work lays a crucial theoretical foundation for solving logical problems involving existential quantifications based on meaning-preserving formula transformation.