Template iterations with non-definable ccc forcing notions
Diego Alejandro Mej\'ia

TL;DR
This paper extends Shelah's iterated forcing theory to non-definable forcing notions, demonstrating its application in constructing models with specific cardinal characteristics and large continuum, including arbitrary regular values for the groupwise-density number.
Contribution
It introduces a version of Shelah's iterated forcing along a template using non-definable forcing notions, expanding the method's applicability.
Findings
Constructed a ccc poset forcing specific cardinal inequalities.
Produced models with large continuum and prescribed groupwise-density number.
Extended Shelah's theory to non-definable forcing notions.
Abstract
We present a version with non-definable forcing notions of Shelah's theory of iterated forcing along a template. Our main result, as an application, is that, if is a measurable cardinal and are uncountable regular cardinals, then there is a ccc poset forcing . Another application is to get models with large continuum where the groupwise-density number assumes an arbitrary regular value.
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