Results 1 
3 of
3
Reflections on reflections in explicit mathematics
 Ann. Pure Appl. Logic
, 2005
"... We give a broad discussion of reflection principles in explicit mathematics, thereby addressing various kinds of universe existence principles. The prooftheoretic strength of the relevant systems of explicit mathematics is couched in terms of suitable extensions of KripkePlatek set theory. 1 ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
We give a broad discussion of reflection principles in explicit mathematics, thereby addressing various kinds of universe existence principles. The prooftheoretic strength of the relevant systems of explicit mathematics is couched in terms of suitable extensions of KripkePlatek set theory. 1
Presentation to the panel, “Does mathematics need new axioms?”
"... The point of departure for this panel is a somewhat controversial paper that I published in the American Mathematical Monthly under the title “Does mathematics need new axioms? ” [4]. The paper itself was based on a lecture that I gave in 1997 to a joint session of the American Mathematical Society ..."
Abstract
 Add to MetaCart
The point of departure for this panel is a somewhat controversial paper that I published in the American Mathematical Monthly under the title “Does mathematics need new axioms? ” [4]. The paper itself was based on a lecture that I gave in 1997 to a joint session of the American Mathematical Society and the Mathematical Association of America, and it was thus written for a general mathematical audience. Basically, it was intended as an assessment of Gödel’s program for new axioms that he had advanced most prominently in his 1947 paper for the Monthly, entitled “What is Cantor’s continuum problem? ” [7]. My paper aimed to be an assessment of that program in the light of research in mathematical logic in the intervening years, beginning in the 1960s, but especially in more recent years. In my presentation here I shall be following [4] in its main points, though enlarging on some of them. Some passages are even taken almost verbatim from that paper where convenient, though of course all expository background material that was necessary there for a general audience is omitted. 1 For a logical audience I have written before about
unknown title
"... This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or sel ..."
Abstract
 Add to MetaCart
This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit: