8 citations · 25 across the 6 of their papers we have counts for
6 papers
Effective cardinals in the nonstandard universe
Vladimir Kanovei, Michael Reeken
We study the structure of effective cardinals in the nonstandard set universe of Hrbacek set theory HST. Some results resemble those known in descriptive set theory in the domain o…
Some new results on Borel irreducibility of equivalence relations
Vladimir Kanovei, Michael Reeken
We prove that orbit equivalence relations (ERs, for brevity) of generically turbulent Polish actions are not Borel reducible to ER s of a family which includes Polish actions of S_…
Borel and countably determined reducibility in nonstandard domain
Vladimir Kanovei, Michael Reeken
We consider reducibility of equivalence relations (ERs, for brevity), in a nonstandard domain, in terms of the Borel reducibility and the countably determined (CD, for brevity) red…
What internal set theory knows about standard sets
Vladimir Kanovei, Michael Reeken
We characterize those standard models M of ZFC which are embeddable, as the class of all standard sets, in a model of internal set theory IST. The necessary and sufficient conditio…
A nonstandard proof of the Jordan curve theorem
Vladimir Kanovei, Michael Reeken
A new elementary nonstandard proof of the Jordan curve theorem is given. The proof (the technical part consists of 4 pages) is self-contained, except for the Jordan theorem for pol…
Isomorphism property in nonstandard extensions of ZFC universe
Vladimir Kanovei, Michael Reeken
We study models of HST, a nonstandard set theory which includes, in particular, the ZFC Replacement and Separation schemata in the language containing the membership and standardne…