Transfinite inductions producing coanalytic sets

• Autorzy: Zoltán Vidnyánszky
• Języki publikacji: EN

Abstrakty

EN

A. Miller proved the consistent existence of a coanalytic two-point set, Hamel basis and MAD family. In these cases the classical transfinite induction can be modified to produce a coanalytic set. We generalize his result formulating a condition which can be easily applied in such situations. We reprove the classical results and as a new application we show that consistently there exists an uncountable coanalytic subset of the plane that intersects every C¹ curve in a countable set.

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 03E15: Descriptive set theory
• 03E45: Inner models, including constructibility, ordinal definability, and core models
• 28A05: Classes of sets (Borel fields, σ -rings, etc.), measurable sets, Suslin sets, analytic sets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2014
• Tom: 224
• Numer: 2
• Strony: 155-174

Daty

wydano

2014

Twórcy

autor

Zoltán Vidnyánszky

• Institute of Mathematics, Eötvös Loránd University, Pázmány Péter s. 1/c, Budapest 1117, Hungary

Identyfikatory

DOI

10.4064/fm224-2-2