Philosophy Lexicon of Arguments

Proof Theory: mathematics, logic is about the existence or nonexistence of finite strings of symbols allowing to derive a statement. Therefore, proof theory is a part of the syntax, as opposed to the model theory, which belongs to the semantics. See also model theory, syntax, semantics.
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Books on Amazon
I 100
Object language / / meta language / Field: e.g. proof theory: there is no object level - object level: here the statements are without reference to sentences or formulas - and not on axioms, rules of inference or derivatives - proof theory: working with math. entities -

Fie I
H. Field
Realism, Mathematics and Modality Oxford New York 1989

Fie II
H. Field
Truth and the Absence of Fact Oxford New York 2001

H. Field
Science without numbers Princeton New Jersey 1980

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Ed. Martin Schulz, access date 2017-05-29