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(2018) Jaakko Hintikka on knowledge and game-theoretical semantics, Dordrecht, Springer.
Borel$$^{*}$$ sets in the generalized baire space and infinitary languages
Tapani Hyttinen, Vadim Kulikov
pp. 395-412
We start by giving a survey to the theory of ({ ext {Borel}}^{*}(kappa )) sets in the generalized Baire space ({ ext {Baire}}(kappa )=kappa ^{kappa }). In particular we look at the relation of this complexity class to other complexity classes which we denote by ({ ext {Borel}}(kappa )), ({Delta _1^1}(kappa )) and ({Sigma _1^1}(kappa )) and the connections between ({ ext {Borel}}^*(kappa )) sets and the infinitely deep language id="IEq8">(M_{kappa ^+kappa }). In the end of the paper we will prove the consistency of ({ ext {Borel}}^{*}(kappa ) e Sigma ^{1}_{1}(kappa )).
Publication details
DOI: 10.1007/978-3-319-62864-6_16
Full citation:
Hyttinen, T. , Kulikov, V. (2018)., Borel$$^{*}$$ sets in the generalized baire space and infinitary languages, in H. Van Ditmarsch & P. Sandu (eds.), Jaakko Hintikka on knowledge and game-theoretical semantics, Dordrecht, Springer, pp. 395-412.
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