Gg Odel's Dialectica Interpretation and Its Two-way Stretch*

Gg Odel's Functional (\dialectica") Interpretation

Gödel's Dialectica Interpretation and Its Two-Way Stretch

In 1958, Gödel published in the journal Dialectica an interpretation of intuitionistic number theory in a quantifier-free theory of functionals of finite type; this subsequently came to be known as Gödel’s functional or Dialectica interpretation. The article itself was written in German for an issue of that journal in honor of Paul Bernays’ 70 birthday. In 1965, Bernays told Gödel of a plan to ...

Scattered Toposes 1

A class of toposes is introduced and studied, suitable for semantical analysis of an extension of the Heyting predicate calculus admitting GG odel's provability interpretation .

Embedding Logics into Product Logic

We construct a faithful interpretation of Lukasiewicz's logic in the product logic (both propositional and predicate). Using known facts it follows that the product predicate logic is not recursively axiomatizable. We prove a completeness theorem for the product logic extended by a unary connective 4 of Baaz 1]. We show that GG odel's logic is a sublogic of this extended product logic. We also ...

Cartesian closed Dialectica categories

When Gödel developed his functional interpretation, also known as the Dialectica interpretation, his aim was to prove (relative) consistency of first order arithmetic by reducing it to a quantifier-free theory with finite types. Like other functional interpretations (e.g. Kleene’s realizability interpretation and Kreisel’s modified realizability) Gödel’s Dialectica interpretation gives rise to ...