[FOM] More new axioms for set theory

[MartDowd at aol.com]

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.
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