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Constructivism and Proof Theory
, 2003
"... 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. F ..."
Abstract

Cited by 162 (4 self)
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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 socalled Gentzen systems which use
sequents instead of formulas and his result on firstorder arithmetic showing that
(suitably formalized) transfinite induction up to the ordinal "0 cannot be proved in
firstorder arithmetic.
Recursion on the partial continuous functionals
 Logic Colloquium ’05
, 2006
"... We describe a constructive theory of computable functionals, based on the partial continuous functionals as their intendend domain. Such a task had long ago been started by Dana Scott [28], under the wellknown abbreviation ..."
Abstract

Cited by 7 (5 self)
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We describe a constructive theory of computable functionals, based on the partial continuous functionals as their intendend domain. Such a task had long ago been started by Dana Scott [28], under the wellknown abbreviation