5 papers
The strong Spector-Gandy Theorem for the higher analytical pointclasses
Joan R. Moschovakis, Yiannis N. Moschovakis
Assuming projective determinacy, we extend Spector's strong version of the Spector-Gandy Theorem to all odd levels of the projective hierarchy: Theorem. For every space which i…
Solovay's Relative Consistency Proof for FIM and BI
Joan Rand Moschovakis
In 2002 Robert Solovay proved that a subsystem BI of classical second order arithmetic, with bar induction and arithmetical countable choice, can be negatively interpreted in the n…
Calibrating the negative interpretation
Joan Rand Moschovakis
The minimum classical extension S of a classically sound theory S based on intuitionistic logic, defined by adding to S the Gentzen negative interpretations of its mathemati…
Intuitionistic Mathematics and Logic
Joan R. Moschovakis, Garyfallia Vafeiadou
The first seeds of mathematical intuitionism germinated in Europe over a century ago in the constructive tendencies of Borel, Baire, Lebesque, Poincaré, Kronecker and others. The f…
Note on -LEM, -LEM and -DNE
Joan R. Moschovakis
We show that results of Akama, Berardi, Hayashi and Kohlenbach, on the relative independence of certain arithmetical principles over intuitionistic arithmetic HA, hold also over Kl…