8 citations · 20 across the 8 of their papers we have counts for
8 papers
Intuitionistic nonstandard bounded modified realisability and functional interpretation
Bruno Dinis, Jaime Gaspar
We present a bounded modified realisability and a bounded functional interpretation of intuitionistic nonstandard arithmetic with nonstandard principles. The functional interpretat…
Todas as afirmações verdadeiras são demonstráveis
Jaime Gaspar
In this instructional exposition in Portuguese for the popularisation of mathematics, we state and prove the completeness theorem.
Copies of classical logic in intuitionistic logic
Jaime Gaspar
Classical logic (the logic of non-constructive mathematics) is stronger than intuitionistic logic (the logic of constructive mathematics). Despite this, there are copies of classic…
A theorem with constructive and non-constructive proofs
Jaime Gaspar
We present a very simple example of a theorem with constructive and non-constructive proofs: the equation c^2 x^2 - (c^2 + c)x + c = 0 has a solution.
Variants into minimal logic of the Kuroda negative translation
Jaime Gaspar
The Kuroda negative translation translates classical logic only into intuitionistic logic, not into minimal logic. We present eight variants of the Kuroda negative translation that…
Negative translations not intuitionistically equivalent to the usual ones
Jaime Gaspar
We refute the conjecture that all negative translations are intuitionistically equivalent by giving two counterexamples. Then we characterise the negative translations intuitionist…