FYI, dateline today:
Posted to the www.dialectics.org website -- E.D. Brief #7 by the new guest author, whose "pen name" is "J2Y' [not a member of F.E.D.], which describes a pathway to core properties that distinguish the third stage/system of the dialectic within the Q_, purely-qualitative dialectical arithmetics -- namely, to the Z-numbers-based, or Integers-based, stage/system, denoted by ZQ_ -- from the second stage/system of that dialectical presentation / argument -- the Whole-numbers-based stage/system, denoted by WQ_.
F.E.D. presents their 'meta-systematic Goedelian dialectic' systems-progression of the [axiomatic] systems of the standard arithmetics in the following order [using X to represent the axiomatic system of the number-space X] --
N ---) W ---) Z ---) Q ---) R ---) C ---) H ---) O ---) ...
-- and so also presents their 'meta-systematic Goedelian dialectic' of the progression of axiomatic systems going on "inside" the Q_ 'meta-system' of their non-standard, 'first dialectical arithmetic systems', in the corresponding order --
NQ_ ---) WQ_ ---) ZQ_ ---) QQ_ ---) RQ_ ---) CQ_ ---) HQ_ ---) ....
The new guest author has already contributed E.D. Brief #5 [only 7 pages], showing a new -- perhaps easier -- pathway to the NQ_ <<arche'>> dialectical arithmetic, and E.D. Brief #6 [only 8 pages], deriving the WQ_ arithmetic from the NQ_ arithmetic. The latest Brief, just posted today -- E.D. Brief #7 -- derives the ZQ_ dialectical arithmetic, from the WQ_ arithmetic.
The "determinateness", or features-richness -- the repleteness of the number-kinds and of the number-sub-kinds 'ideo-ontology' -- of each successor system of arithmetic in that dialectical systems-progression is greater than that of all of its predecessor systems.
This is reflected in the fact that the derivation of the ZQ_ axioms-system -- which has the richest number-ontology yet in that progression -- took 19 pages!
Link to Webmaster's notice for this new posting: Webmasters Notice for E.D. Brief # 7
Link to the F.E.D. Secretary-General's F.E.D. Preface to E.D. Brief #7: E.D. Brief #7
Link to F.E.D. Preface to E.D. Brief #7: F.E.D. Preface to E. D. Brief #7
Link to E.D. Brief #6: E.D. Brief #6
Link to E.D. Brief #5: E.D. Brief #5
Link to F.E.D. Preface to E.D. Brief #5: F.E.D. Preface to E. D. Brief #5
These introductory Briefs by J2Y are believed to be more readily accessible than are the standard F.E.D. primers on these dialectical arithmetics [even though the third Brief in that series, just posted, could no longer be, owing to the nature/richness of its content, as "brief" as the earlier two]. Enjoy!!!