Weakly represented families in reverse mathematics

Rupert Hölzl, Dilip Raghavan, Frank Stephan, Jing Zhang

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We study the proof strength of various second order logic principles that make statements about families of sets and functions. Usually, families of sets or functions are represented in a uniform way by a single object. In order to be able to go beyond the limitations imposed by this approach, we introduce the concept of weakly represented families of sets and functions. This allows us to study various types of families in the context of reverse mathematics that have been studied in set theory before. The results obtained witness that the concept of weakly represented families is a useful and robust tool in reverse mathematics.

Original languageEnglish
Pages (from-to)160-187
Number of pages28
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
StatePublished - 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© Springer International Publishing AG 2017.


R. Hölzl and F. Stephan were supported in part by MOE/NUS grants R146-000-181-112 and R146-000-184-112 (MOE2013-T2-1-062); D. Raghavan was supported in part by MOE/NUS grant R146-000-184-112 (MOE2013-T2-1-062). Work on this article begun as J. Zhang’s Undergraduate Research Opportunities Programme project while J. Zhang was an undergraduate students of NUS and R. Hölzl worked at NUS financed by MOE/NUS grant R146-000-184-112 (MOE2013-T2-1-062).

FundersFunder number
National University of SingaporeMOE2013-T2-1-062, R146-000-184-112, R146-000-181-112


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