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In this paper, we present three methods to give the value of a classical integer in
-calculus. The first method is an external method and gives the value and the false part of a normal classical integer. The second method uses a new reduction rule and gives as result the...
We give a proof of Hechler's theorem that any
-directed partial order can be embedded via a ccc forcing notion cofinally into
ordered by eventual dominance. The proof relies on the standard forcing relation rather than the variant introduced by Hechler.
Coherence-spaces and domains with totality are used to give interpretations of inductively defined types. A category of coherence spaces with totality is defined and the closure of positive inductive type constructors is analysed within this category. Type streams are introduced as a...
We shall prove the second incompleteness theorem via Kolmogorov complexity.
This research was partially supported by Grant-in-Aid for Scientific Research (No. 06640178 and No. 06640336), Ministry of Education, Science and Culture of Japan Mathematics Subject Classification: 03E05 -->
Abstract. Following Carr's study on diagonal operations and normal filters on
We estimate the derivation lengths of functionals in Gödel's system
of primitive recursive functionals of finite type by a purely recursion-theoretic analysis of Schütte's 1977 exposition of Howard's weak normalization proof for
. By using collapsing techniques from Pohlers' local...
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