Prikry Forcing and Tree Prikry Forcing of Various Filters
Tom Benhamou
TL;DR
This paper explores Prikry forcing and Tree Prikry forcing with various filters, addressing open questions and providing comprehensive proofs of known theorems in the context of set theory and forcing techniques.
Contribution
It introduces new insights into Tree Prikry forcing with different filters and offers detailed proofs, enhancing understanding of Prikry-type forcings.
Findings
Answered an open question about Mathias criteria for Tree-Prikry forcing
Investigated Prikry forcing with various filters
Provided detailed proofs of known theorems
Abstract
In this paper, we answer a question asked in "A minimal Prikry type forcing for singularizing a measurable cardinal" regarding a Mathias criteria for Tree-Prikry forcing. Also we will investigate Prikry forcing using various filters. For completeness and self inclusion reasons, we will give proofs of many known theorems.
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