UNIVERSAL FUNCTIONS IN PARTIAL STRUCTURES | Zendy

Negri Maurizio | Zendy

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UNIVERSAL FUNCTIONS IN PARTIAL STRUCTURES

Author(s) -

Negri Maurizio

Publication year - 1992

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/malq.19920380121

Subject(s) - recursion (computer science) , partial function , mathematics , simple (philosophy) , class (philosophy) , universal turing machine , pure mathematics , algebra over a field , computer science , discrete mathematics , algorithm , turing machine , computation , artificial intelligence , philosophy , epistemology

In this work we show that every structure can be expanded to a partial structure * with universal functions for the class of polynomials on *. We can embed * monomorphically in a total structure º that preserves universal functions of * and that is universal among such structures, i.e. º can be homomorphically embedded in every total structure that preserves universal functions of *. Universal functions are the starting point for developing recursion theoretic tools in an * that satisfies some simple additional conditions.

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