Definable tree property for uncountable regular cardinals

Mohammad Golshani; Mostafa Mirabi

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arXiv · 1608.06727

Definable tree property for uncountable regular cardinals

Mohammad Golshani·Mostafa Mirabi

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Abstract

The primary goal of this paper is to establish a model of $ZFC$ wherein the definable tree property is affirmed for all uncountable regular cardinals. This endeavor commences with the utilization of both a supercompact cardinal and a measurable cardinal that exceeds it. Subsequently, we construct a $ZFC$ model. Within this model, we demonstrate that the definable tree property holds for all uncountable regular cardinals. Thereby we respond to an inquiry raised in [1].

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Mohammad Golshani, Mostafa Mirabi. 2016-08-24. Definable tree property for uncountable regular cardinals. https://arxiv.org/abs/1608.06727

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