Request for Reference/Link to example of defining a theory/logic.

Hi:

I am requesting help in locating a link or reference showing an example
of defining a theory and/or logic. I am constructing a formal system
that will emulate first-order logic and set theory. I am unsure what is
the minimum theorem/proofs necessary to demonstrate that the formal
system does indeed include first-order logic and set theory. Does
anyone know of a web reference or book that dwelves into this topic?
Thanks.

Regards,
Scott

.

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