Constructivism and Proof Theory

Constructivism and Proof Theory (2003)

by A. S. Troelstra

Citations:

135 - 4 self

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Datum	Value	Source
TITLE	Constructivism and Proof Theory	user correction - Legacy Corrections
AUTHOR NAME	A. S. Troelstra	user correction
ABSTRACT	Introduction to the constructive point of view in the foundations of mathematics, in particular intuitionism due to L.E.J. Brouwer, constructive recursive mathematics due to A.A. Markov, and Bishop’s constructive mathematics. The constructive interpretation and formalization of logic is described. For constructive (intuitionistic) arithmetic, Kleene’s realizability interpretation is given; this provides an example of the possibility of a constructive mathematical practice which diverges from classical mathematics. The crucial notion in intuitionistic analysis, choice sequence, is briefly described and some principles which are valid for choice sequences are discussed. The second half of the article deals with some aspects of proof theory, i.e., the study of formal proofs as combinatorial objects. Gentzen’s fundamental contributions are outlined: his introduction of the so-called Gentzen systems which use sequents instead of formulas and his result on first-order arithmetic showing that (suitably formalized) transfinite induction up to the ordinal "0 cannot be proved in first-order arithmetic.	user correction
YEAR	2003	user correction - Legacy Corrections
CITATIONS	27 found	ParsCit 1.0