Intuitionism — Counting its Blessings. Preliminary version

Intuitionism { Counting its Blessings . Preliminary

A brief survey of the impact of intuitionistic logic and mathematics on modern practice is presented. The main in uence is via the so-called \BHK interpretation" (or \proof interpretation"). By somewhat relaxing the conditions on the notion of proof the familiar notions of `realizability', `Curry-Howard isomorphism' etc. are motivated. Also some attention is paid to the characteristic process o...

Intuitionism - Counting its Blessings

A brief survey of the impact of intuitionistic logic and mathematics on modern practice is presented. The main influence is via the so-called “BHK interpretation” (or “proof interpretation”). By somewhat relaxing the conditions on the notion of proof the familiar notions of ‘realizability’, ‘Curry-Howard isomorphism’ etc. are motivated. Also some attention is paid to the characteristic process ...

Intuitionism

Preliminary Version

The main theorem of this paper is that, for every real number < 1 (e.g., = 0:99), only a measure 0 subset of the languages decidable in exponential time are Pn tt-reducible to languages that are not exponentially dense. Thus every Pn tt-hard language for E is exponentially dense. This strengthens Watanabe's 1987 result, that every PO(logn) tt-hard language for E is exponentially dense. The comb...

Preliminary Version