An ordinal-connection axiom as a weak form of global choice under the GCH

Archive for Mathematical Logic 62 (3):321-332 (2022)
  Copy   BIBTEX


The minimal ordinal-connection axiom $$MOC$$ was introduced by the first author in R. Freire. (South Am. J. Log. 2:347–359, 2016). We observe that $$MOC$$ is equivalent to a number of statements on the existence of certain hierarchies on the universe, and that under global choice, $$MOC$$ is in fact equivalent to the $${{\,\mathrm{GCH}\,}}$$. Our main results then show that $$MOC$$ corresponds to a weak version of global choice in models of the $${{\,\mathrm{GCH}\,}}$$ : it can fail in models of the $${{\,\mathrm{GCH}\,}}$$ without global choice, but also global choice can fail in models of $$MOC$$.



    Upload a copy of this work     Papers currently archived: 92,197

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

The theorem of the means for cardinal and ordinal numbers.George Rousseau - 1993 - Mathematical Logic Quarterly 39 (1):279-286.
On generic extensions without the axiom of choice.G. P. Monro - 1983 - Journal of Symbolic Logic 48 (1):39-52.
Factors of Functions, AC and Recursive Analogues.Wolfgang Degen - 2002 - Mathematical Logic Quarterly 48 (1):73-86.
Rigit Unary Functions and the Axiom of Choice.Wolfgang Degen - 2001 - Mathematical Logic Quarterly 47 (2):197-204.
Forms of the Pasch axiom in ordered geometry.Victor Pambuccian - 2010 - Mathematical Logic Quarterly 56 (1):29-34.
Choice principles from special subsets of the real line.E. Tachtsis & K. Keremedis - 2003 - Mathematical Logic Quarterly 49 (5):444.
Von Rimscha's Transitivity Conditions.Paul Howard, Jean E. Rubin & Adrienne Stanley - 2000 - Mathematical Logic Quarterly 46 (4):549-554.


Added to PP

8 (#1,322,157)

6 months
5 (#647,370)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

Powers of regular cardinals.William B. Easton - 1970 - Annals of Mathematical Logic 1 (2):139.

Add more references