Syntax, semantics, and the problem of the identity of mathematical objects

Philosophy of Science 55 (3):376-386 (1988)
A plurality of axiomatic systems can be interpreted as referring to one and the same mathematical object. In this paper we examine the relationship between axiomatic systems and their models, the relationships among the various axiomatic systems that refer to the same model, and the role of an intelligent user of an axiomatic system. We ask whether these relationships and this role can themselves be formalized
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