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epsilon calculus
Hilbert's epsilon calculus is an extension of a formal language by the epsilon operator, where the epsilon operator substitutes for quantifiers in that language as a method leading to a proof of consistency for the extended formal language. The ''epsilon operator'' and ''epsilon substitution method'' are typically applied to a first-order predicate calculus, followed by a showing of consistency. The epsilon-extended calculus is further extended and generalized to cover those mathematical objects, classes, and categories for which there is a desire to show consistency, building on previously-shown consistency at earlier levels.〔Stanford, overview paragraphs〕
==Epsilon operator==
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