Generalized Silver and Miller measurability
Generalized Silver and Miller measurability Giorgio Laguzzi May 10, 2014 Abstract We present some results about the burgeoning research area concerning set theory of the “κ-reals”. We focus on some notions of measurability coming from generalizations of Silver and Miller trees. We present analogies and mostly differences from the classical setting. 1
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Introduction and basic definitions
The study of the generalized version of the Baire space κκ and Cantor space 2κ , for κ uncountable regular cardinal, is a burgeoning research area, which intersects both the generalized descriptive set theory and the set theory of the “κ-reals”, where we refer to the elements of κκ and 2κ as κ-reals. Basic Notation. The dramatis personae of our work are the so-called tree-like forcings. A tree T is a subset of either 2
1
Introduction and basic definitions
The study of the generalized version of the Baire space κκ and Cantor space 2κ , for κ uncountable regular cardinal, is a burgeoning research area, which intersects both the generalized descriptive set theory and the set theory of the “κ-reals”, where we refer to the elements of κκ and 2κ as κ-reals. Basic Notation. The dramatis personae of our work are the so-called tree-like forcings. A tree T is a subset of either 2
