Avoidable polynomials and R ⊆ L
نویسنده
چکیده
In [3, 4] Törnquist and Weiss proved many natural Σ2 definable counterparts of classical equivalences to the Continuum Hypothesis (CH). These become equivalent to “all reals are constructible”. Following this scheme, we proved definable counterparts for some algebraic equivalent form of CH. More specifically we obtained a Σ2 version of a result about avoidable polynomials proven by Schmerl [2]. As a corollary, we have R ⊆ L if and only if there exists a Σ2 coloring of the plane in countably many colors with no monochromatic right-angled triangle, which is the Σ2 analogous of a famous result by Erdős and Komjáth [1].
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