Intrinsic Justifications for Large-Cardinal Axioms

DOI10.1093/PHILMAT/NKAA038zbMATH Open1505.03100arXiv1403.8058OpenAlexW3148679419WikidataQ114631625 ScholiaQ114631625MaRDI QIDQ5067709

Rupert McCallum

Publication date: 4 April 2022

Published in: Philosophia Mathematica (Search for Journal in Brave)

Abstract: William Tait and Peter Koellner have written on the topic of which reflection principles are intrinsically justified. Phillip Welch and Sam Roberts have recently sought to motivate much stronger reflection principles. This work also had some similarities with previous work of Victoria Marshall's on reflection principles, as may be seen from considerations which we will seek to articulate in what follows. The statement of our three philosophical theses shall be given in the Introduction. We will present a set of technical results in support of three philosophical theses which will be articulated at the end of the Introduction.

Full work available at URL: https://arxiv.org/abs/1403.8058

Mathematics Subject Classification ID

Philosophical and critical aspects of logic and foundations (03A05) Large cardinals (03E55)