Abstract
A first-order formula q5(xl,xn)is called“geometric”if it is built up from atomic formulas by using conjunction,disjunction,and existential quantification,Geometric logic is the logic of the implications between geometric formulas:
where the arrow here is for “implication” and and z/) are geometric. Many mathematical structures can be axiomatized by formulas of this form (1).For instance, local rings are axiomatized by the usual equations for a commutative ring with unit, together with the axiom
which states that the ring is local; this axiom (2) is indeed of the form (1).
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© 1994 Springer Science+Business Media New York
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Mac Lane, S., Moerdijk, I. (1994). Geometric Logic and Classifying Topoi. In: Sheaves in Geometry and Logic. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0927-0_12
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DOI: https://doi.org/10.1007/978-1-4612-0927-0_12
Publisher Name: Springer, New York, NY
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