[FOM] Foreman's preface to HST

A. Mani a_mani_sc_gs at yahoo.co.in
Wed Apr 28 20:14:06 EDT 2010

On Tuesday 27 Apr 2010 12:46:27 pm joeshipman at aol.com wrote:
> This is merely a practical observation; if you know of any serious
> mathematical investigation of questions which can be stated in the
> language of set theory that cannot easily be conducted in the framework
> of first-order-logic + ZFC, I'd like to hear about it.

Formal versions of semi set theory would be conservative extensions of ZF.
So much of Semi-set theory* and its formal versions would fit into that. From 
the practical point of view it has already been applied in mathematical 
investigations of linguistics (see Novak's book). From the computation point 
of view it is better.

* The original version of semi set theory as in the 1971-2 book of Vopenka and 
Hajek has plenty of philosophical considerations and that can taken as an 
informal theory. 
An interesting introduction to semisets is at 
(it does not attempt to look at the philosophical parts in any detail though.)

What exactly do you mean by 'easily'? 
Plenty of Mathematics would look fairly terrible if written in FOL+ZFC. 


A. Mani  

A. Mani

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