Hello,

there is a famous quoatation of David Hilbert:

„Aus dem Paradies, das Cantor uns geschaffen, soll uns niemand vertreiben können.“
(From the paradise, that Cantor created for us, no-one shall be able to expel us.)
Hilbert (1926, p. 170), a lecture given in Münster to Mathematical Society of Westphalia
on 4 June 1925

Most mathematicans still seem to have similar opinions to David Hilbert and have no problems
with different kinds of infinity.

To me modern set theories like ZFC are no paradise, but they remind me of Ptolemaic epicyclics
when leading to infinite kinds of infinities and cardinal numbers.
So I had a look around how to get things more easy and plausible.

The diagonalization of Cantor leads to the way out:
Of course the proof is correct, but it uses the classical logic.

With a new logic the proof might work no more.
And I did not go for constructive / intuonistic logic, as this was already discussed in Hilbert`s time.

I have developed a new logic, the layer logic and a new layer set theory.
They not only invalidaded the diagonalization proof
but also helped with a lot of paradoxes / antinomies.

With layer logic / set theorie we only have one kind of infinity,
the countable infinity of the natural numbers.
The Russell set and the set of all sets are both (ordinary) sets.

The main “trick” of the new layer logic are the layers: A proposition is not true or false,
but only true or false in a layer (0,1,2, ...)

This layers were first just a formal parameter to differentiate truth values
(for example in the first part of a proof and the second).
Meanwhile I see them as a kind of a new dimension, of meta levels or cause and effect order
or a new part of time.

Even without knowing exactly what a layer is, we can use layer logic and layer set theorie,
as the rules for using them are mostly independent of this.

Here links with more detailed information about layer logic und layer set theory:
www.researchgate.net/post/Is_this_a_new_valid_logic_And_what_does_layer_logic_mean
In German: www.ask1.org/threads/stufenlogik-trestone-reloaded-vortrag-apc.17951/#post-492741

As it is unusual and bulky I can understand that not many are going to study it,
but in my eyes the possible results – a new look on logic and the world
and out of Hilbert`s Paradise- it is worth the effort.

On the other hand I am interested to learn, why Hilbert`s (or Cantor`s) paradise is so attractive?

Yours Trestone