[FOM] A query on explicit definitions of inacessible cardinals.

[Frode Bjørdal]

I am skeptical about the existence of relative inaccessible cardinals for
which one cannot give a precise explicit definition in terms of its set
condition in the language of set theory, or a slight extension thereof in
librationism £ as I prefer (see http://arxiv.org/abs/1407.3877 and
http://apcz.pl/czasopisma/index.php/LLP/article/view/LLP.2012.016). In a
question at Mathoverflow (
http://mathoverflow.net/questions/199850/a-query-on-how-to-climb-inaccessibles-in-%C2%A3
<http://mathoverflow.net/questions/199850/a-query-on-how-to-climb-inaccessibles-in-£>)
I give such an explicit definition for Mahlo-cardinals by means of a fixed
point construction I call manifestation point (it goes back to Cantini and
Visser and is related to work by Kleene and, ultimately, Gödel) in the
librationist framework. With additional assumptions giving us £M this means
that we can have an interpretation of ZFC+Mahlo (in the sense isolated) in
£M; we then follow the strategy I use in http://arxiv.org/abs/1407.3877 to
isolate an interpretation of ZFC in £ + the Skolem-Fraenkel Postulation.

 It seems to me, and also from the literature, that it is dubious that we
can press such a justification as this of inaccessible cardinals much
higher. Can a limit be pinpointed?

​Best regards

Frode​


..........................................
Professor Dr. Frode Bjørdal
Universitetet i Oslo Universidade Federal do Rio Grande do Norte
quicumque vult hinc potest accedere ad paginam virtualem meam
<http://www.hf.uio.no/ifikk/personer/vit/fbjordal/index.html>
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