Intuitionism and Effective Descriptive Set Theory

Classical descriptive set theory as a refinement of effective descriptive set theory

The (effective) Suslin-Kleene Theorem is obtained as a corollary of a standard proof of the classical Suslin Theorem, by noticing that it is mostly constructive and applying to it a naive realizability interpretation. Effective Descriptive Set Theory is advertized as a refinement of the classical theory of definability (on Polish spaces) developed in the first half of the 20th century, for exam...

Towards Synthetic Descriptive Set Theory: An instantiation with represented spaces

Using ideas from synthetic topology, a new approach to descriptive set theory is suggested. Synthetic descriptive set theory promises elegant explanations for various phenomena in both classic and effective descriptive set theory. Presently, we mainly focus on developing the ideas in the category of represented spaces.

Logic Column 18: Alternative Logics: A Book Review

A few years ago, Bill Gasarch, editor of the Book Review Column, sent me a copy of the book Alternative Logics: Do Sciences Need Them? [28], edited by Paul Weingartner, and asked if I was interested in reviewing it. The book is a collection of essays discussing whether there is a need for logics other than classical logic in various areas of science. Interestingly, I had just finished reading a...

Notes on Effective Descriptive Set Theory

Alternative Logics: A Book Review

A few years ago, Bill Gasarch, editor of the Book Review Column, sent me a copy of the book Alternative Logics: Do Sciences Need Them? [28], edited by Paul Weingartner, and asked if I was interested in reviewing it. The book is a collection of essays discussing whether there is a need for logics other than classical logic in various areas of science. Interestingly, I had just finished reading a...