Comparing forcing approaches to dense ideals

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This is a Experimental Study study.

Monroe Eskew

doi:10.48550/arxiv.2503.00964

March 2, 2025Open Access

Comparing forcing approaches to dense ideals

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Key Points

The study finds that the Anonymous Collapse is equivalent to the Dual Shioya Collapse for collapsing a large cardinal.
It demonstrates a new method for constructing a normal ideal on omega_2 that relates to collapsing techniques.
The analysis involves certain posets, contributing to the understanding of forcing constructions in set theory.
These findings may influence future studies on dense ideals and their applications in set theory.

Implication

Analysis shows equivalence between Anonymous Collapse and Dual Shioya Collapse for large cardinals, indicating parallels in forcing strategies.

Abstract

We analyze some posets involved in forcing constructions for dense ideals, showing that the Anonymous Collapse and the Dual Shioya Collapse are equivalent for collapsing a large cardinal to ω₂. We also give a somewhat simplified construction of a normal ideal I on ω₂ such that P(ω₂)/I ~ Col(ω₁,ω₂).

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Cite This Study

Monroe Eskew (2025) studied this question.

synapsesocial.com/papers/68ecc715d1cc7436f7d18c64 https://doi.org/10.48550/arxiv.2503.00964

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Comparing forcing approaches to dense ideals

Key Points

Implication

Abstract

Discussion

Cite This Study

Comparing forcing approaches to dense ideals

Key Points

Implication

Abstract

Discussion

Cite This Study

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