Two problems from Tarsky's metatheorem

[Sonnet Nguyen <Sonnet.Nguyen@fuw.edu.pl>]

Dear academics,
By the occasion of presenting Tarsky's metatheorem to public of VNSA, I 
would like to add two interesting questions to all public of VNSA.

Problem1: Find an example of a simple formula with quantifiers in the
          language of field and quantifiers of which are un-removed!

(It's an Aiviet's problem)


Problem2: I define a VNSA-Tarsky's cathegory by following:  
          VNSA-Tarsky's cathegory is a cathegory of algebras
          (algebra in the most general sense: i.e. a set with a family of
          algebraic operations and relations)
          such that each formula is reduced to open formula.
          
An example of VNSA-Tarsky's cathegory is a cathegory of ordered closed (in
the real sense) fields.

Characterize VNSA-Tarsky's cathegory.  Subquestion: Is Cathegory of
Quantum groups  (defined as dual cathegory of the cathegory of Hopf
algebras) VNSA-Tarsky's cathegory ???

(It's 17-th Sonnet's problem)

Awards: 2 bottles of champagnes for solving problems.
        And may be First Medal Fiels for VN??    

enjoys,
SN
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| Sonnet Nguyen,  Polish Acad. of Scie.                 |
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