# [FOM] More new axioms for set theory

MartDowd at aol.com MartDowd at aol.com
Fri Jul 20 13:39:20 EDT 2012

In an earlier posting I referred to my paper
"Some New Axioms of  Set Theory",
IJPAM 66 (2011), no. 2, 121--136,
_http://www.ijpam.eu/contents/2011-66-2/1/1.pdf_
(http://www.ijpam.eu/contents/2011-66-2/1/1.pdf)
This  paper presents a strong justification for accepting axioms I1-I4,
which are  equivalent to Ord being Mahlo; and axioms M1-M4, which are
equivalent to Ord  being hyper-Mahlo.  An axiom called axiom G was
presented,
as reasonable  but not yet fully justified.

I also referred to my paper
"Improved Results in Scheme  Theory"
IJPAM, to appear
_http://www.hyperonsoft.com/irst.pdf_ (http://www.hyperonsoft.com/irst.pdf)
This  paper proves that axiom G is equivalent to Or being greatly Mahlo,
or  $\kappa^+$-Mahlo.  No justfication was presented.

In a new paper,
"Scheme Terms"
Submitted
_http://www.hyperonsoft.com/witz.pdf_ (http://www.hyperonsoft.com/witz.pdf)
a  justification of axiom G is presented.  A justification for a  stronger
axiom, "Ord is $\phi(1,\epsilon_0)$-Mahlo", is presented.  The  issues
involved in proceeding further are clear from the results of the  paper.
-------------- next part --------------
An HTML attachment was scrubbed...
URL: </pipermail/fom/attachments/20120720/ba1225f8/attachment-0001.html>