[FOM] the amazing language of set theory
Tero TULENHEIMO
tero.tulenheimo at univ-lille3.fr
Tue Mar 29 04:03:57 EDT 2016
Charlie Silver wrote:
> Envoyé: Mardi 29 Mars 2016 03:30:33
> Objet: Re: [FOM] the amazing language of set theory
>
> For foundational studies, why not use (a sort of) “function theory” instead
> of set theory (different from Von Neumann’s f’n theory modified by
> Bernays,…) There are different ways to look at f’n theory. I’m proposing
> that the ordered pair <x,y> be the primitive sentence, saying y is a
> function of x.
This proposal sounds pretty much like the starting point of the so-called dependence logic developed by Jouko Vaananen: one takes as primitive the statement that the value of variable x_0 is a function of values of variables x_1,...,x_n. Taken by itself, such a statement will be expressible in existential second-order logic (\Sigma^1_1). Certain extensions of dependence logic reach the expressive power of full second-order logic.
See e.g.
http://www.math.helsinki.fi/logic/people/jouko.vaananen/Dagstuhl10.pdf
http://plato.stanford.edu/entries/logic-if/#DepLog
https://en.wikipedia.org/wiki/Dependence_logic
Tero Tulenheimo
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